Background Independent Quantum Gravity: A Status Report

Abhay Ashtekar; Jerzy lewandowski

REVIEW

Background Independent Quantum Gravity: A Status Report

Abhay Ashtekar, Jerzy Lewandowski

General Relativity and Quantum Cosmology · Submitted 5 Apr 2004 · 190 references

Pith's verdict: A careful, honest map of loop quantum gravity's kinematic core, though the abstract's 'no hidden infinities' line outruns what the dynamics section actually delivers.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 2 major objections · 8 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDgr-qc/0404018 (version 2)

Pith ID4TNFFO35, Pith's permanent record of this paper and its review

CitationAbhay Ashtekar, Jerzy lewandowski. "Background Independent Quantum Gravity: A Status Report." arXiv:gr-qc/0404018 (2004). https://pith.science/paper/4TNFFO35

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

This is the review you want on the shelf if you need to know what loop quantum gravity actually claims, as opposed to what gets attributed to it. The kinematic half — Sections IV and V — is the real contribution: the holonomy-flux algebra, the Ashtekar-Isham-Lewandowski measure as a genuine regular Borel measure on the space of generalized connections, and the area and volume operators as densely defined, essentially self-adjoint operators with discrete spectra and no renormalization. The area gap arithmetic checks out (Eq. 5.15, 4 pi gamma l_Pl^2 sqrt(3/2)), and the paper gives the full spectrum (5.14) rather than the simplified version that gets quoted too often in the secondary literature. That matters; the simplified form is not the general answer and the authors say so explicitly in the remarks after 5.18. Where I would push back is the abstract's claim of 'sufficient mathematical precision to ensure that there are no hidden infinities' [abstract:s6]. That is true of the kinematics, and the paper knows it. In Section VI C 2 the regulator is removed only pointwise on the algebraic dual Cyl*, and the authors themselves write that the habitat 'just turned out to be too small to provide a non-trivial viability criterion' — the commutator of two scalar constraints vanishes there because the quantum analog of the classical bracket also annihilates every state in it. So the one consistency check that would test the quantization is satisfied trivially on the only domain where the operator is known to act. The paper says it is 'likely' the domain is larger and 'may contain semi-classical states'. That is a hope, not a result. Your stress-test note lands, and I would keep it. The entropy count in Section VIII is the other soft spot, and it is inherited rather than introduced here: gamma is fixed by matching S = A/4. The paper is upfront about that. The partial defense is that the same gamma then yields the right coefficient across horizon types, which is more than a one-parameter fit usually buys — but it is not a prediction, and the review should not be read as claiming one. For a review, the citation pattern is appropriate; the self-citation is doing real work rather than padding. Who is it for: a graduate student or a neighboring-field physicist who wants the actual construction, not the slogan. Anyone already in the field will go straight to Sections VI C and IX for the authors' own read on the open problems. Worth referee time? Yes — mainly to check that Sections VII through IX represent the cosmology and entropy literature fairly, since those are the parts where the authors are summarizing other people's work alongside their own.

Referee report

Significance

The review's lasting value is its explicit operator constructions: the area operator (Eqs. 5.4 and 5.14) with smallest nonzero gap 4 pi gamma l_Pl^2 sqrt(3/2) (Eq. 5.15), the volume operator (Eq. 5.21), and the demonstration that these are densely defined, essentially self-adjoint operators on a genuine regular Borel measure space rather than formal functional integrals. The treatment is candid about open problems, notably the regularization ambiguities of the scalar constraint (Section VI C) and the fact that the anomaly-freedom test is vacuous on the habitat. The paper is a standard entry point to the field and its pedagogical value is high; the area-gap arithmetic in Eq. 5.15 checks out (the minimum of -lambda is 3/4 at (j_u, j_d, j_{u+d}) = (1/2, 0, 1/2)).

Major objections (2)

[Abstract [abstract:s6] and Section VI C 2] The abstract's claim [abstract:s6] of 'sufficient mathematical precision to ensure that there are no hidden infinities' is established only for the kinematic framework. In Section VI C 2 the regulator is removed only pointwise on the algebraic dual Cyl* (Eq. 6.36), and the Remark following Eq. 6.40 concedes that the 'habitat' on which the constraint commutator can be tested is 'too small to provide a non-trivial viability criterion.' The authors acknowledge this in the body, so the issue is one of framing rather than of an unstated gap: the abstract should be qualified to say that the absence of hidden infinities is a kinematic result, with the dynamical extension still open. As written, a reader of the abstract alone would take the claim to cover the full theory including dynamics.
[Section I C and Section VIII] Section I C lists 'a statistical mechanical derivation of the horizon entropy' as a headline advance, but the derivation reproduces S_BH = A/4 only after the Barbero-Immirzi parameter gamma is fixed by matching that same formula. The logical status of the result, consistency check versus parameter-free prediction, should be stated explicitly at the point where the claim is made (Section I C and the opening of Section VIII), not only in the later discussion of non-minimal couplings. This is a request about framing of a result the review reports from published work, not a demand that the derivation be reproduced here; the concern is that a reader encountering the claim in Section I C could reasonably take it to be a prediction rather than a fit of one free parameter to one target number.

Minor objections (8)

[Section VII B 2] The text refers to 'the mathematician Harold Bohr, Neils' brother.' The mathematician was Harald Bohr and the physicist was Niels Bohr; both spellings should be corrected.
[Section VII C] 'Lesbegue measure' should read 'Lebesgue measure.'
[Section II C 3 and elsewhere] The parameter is spelled 'Barbero-Immerzi' in Section II C 3 and 'Barbero-Immirzi' elsewhere; the spelling should be standardized throughout.
[Section IV C 5] The sentence 'A generic element of Diﬀ is fails to be analytic' contains a grammatical error and should be corrected.
[Section V B 1, Eq. 5.21] The constant kappa_o is described as 'undetermined' and 'usually set equal to 1.' Since it multiplies the entire volume spectrum, its status should be stated more prominently, and the reader should be told explicitly whether physical results such as the volume gap depend on it.
[Section V A 1, Eq. 5.4] The operator Delta_{S,v,alpha} is called the 'vertex Laplace operator,' which may mislead readers into thinking it is the graph Laplacian; a brief clarification that it is defined by the up/down flux combination of Eq. 5.5 would help.
[Section IV C 1, Eqs. 4.39-4.40] The sign convention kappa(S,e) = plus or minus 1 for edges 'above' or 'below' S would benefit from a figure or an explicit orientation convention, since the subsequent regularization of geometric operators relies on it.
[Section IV C 5 Remark] 'cris-crossing' should read 'criss-crossing.'

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Loop quantum gravity replaces the smooth spacetime continuum with discrete quanta of area and volume, and does so without presupposing any background geometry.

The reading

This review argues that gravity can be quantized without any background spacetime, and that doing so forces geometry itself to become discrete rather than continuous. The authors build the theory in two layers: a kinematical Hilbert space of generalized connections, on which holonomies act by multiplication, and geometric operators for area and volume built out of the conjugate triad fields. The headline result is that these operators have discrete, computable spectra: the area of a surface comes in multiples set by spin labels on the edges piercing it, with a smallest nonzero value of $4�pi�gamma�ell_{Pl}^2�sqrt{3/2}$. If the construction holds, the continuum of general relativity is an approximation, and the infinities that plague perturbative quantum gravity never arise because every step of the construction is finite.

What carries the argument

The load-bearing object is the holonomy-flux algebra: configuration variables are holonomies of an $SU(2)$ connection along piecewise-analytic edges, and momentum variables are fluxes of the conjugate triad across 2-surfaces. Completing the algebra of configuration variables in the sup-norm and applying Gel'fand theory gives a compact quantum configuration space of generalized connections, on which a diffeomorphism-invariant measure exists; this is the arena in which all operators are defined. The geometric operators are then obtained by writing area and volume as limits of Riemann sums of smeared triad fluxes and replacing each flux by its operator. Two technical devices carry the dynamics: the co-triad is written as a Poisson bracket of the connection with the total volume, $e^a_i = 2k�gamma�{A^i_a, V}$, which removes the inverse power of $�det P$ from the scalar constraint, and the extrinsic-curvature term is generated by a nested bracket involving the Euclidean scalar constraint and the volume. The resulting constraint operator acts on diffeomorphism-invariant states by creating and annihilating 'extraordinary' loops at vertices.

Extended reading notes

Core claim

The paper's central claim is that general relativity, recast as a dynamical theory of connections with a compact structure group, admits a background-independent quantization in which Riemannian geometry itself becomes a quantum observable with discrete eigenvalues. The authors construct a Hilbert space of square-integrable functions on a space of generalized connections, show that the Haar measure used is invariant under diffeomorphisms, and then regularize the area and volume functionals of the classical phase space into self-adjoint operators whose spectra are discrete and explicitly computable. Around this core they assemble the surrounding results: the Gauss and diffeomorphism constraints are solved exactly (the latter by group averaging, with solutions living in the dual of the space of cylindrical functions), the scalar Hamiltonian constraint is given a well-defined regularized action on diffeomorphism-invariant states, and the framework is applied to homogeneous cosmology, where the inverse scale factor and curvature acquire upper bounds, and to isolated horizons, where counting surface states yields an entropy proportional to horizon area.

Load-bearing premise

The whole edifice rests on the assumption that the unique diffeomorphism-invariant representation of the holonomy-flux algebra is the physically correct stage for quantum dynamics, a choice justified by general covariance rather than by any dynamical test, so the discreteness results are kinematic until the constraint operators built on that stage are shown to admit realistic semiclassical states.

Editorial extensions

If this is right

Black hole entropy is derived statistically: counting the spin-network states of a quantum horizon reproduces an area law, with the Barbero-Immirzi parameter fixed to a specific numerical value by matching the coefficient.
In homogeneous, isotropic loop quantum cosmology the operator corresponding to the inverse scale factor is bounded above, so curvature and matter Hamiltonians stay finite where classical general relativity predicts a big-bang singularity.
Quantum Einstein's equations acquire a precise operator meaning, unlike in geometrodynamics, where products of the Wheeler-DeWitt operators remain formal.
The same framework yields a background-independent path-integral formulation through spin-foam models, built from the same spin-network labels.
Low-energy physics must emerge from a sufficient supply of semiclassical states, and the paper identifies constructing these states as the main open problem for connecting the Planck-scale description to ordinary physics.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If area is genuinely discrete with a fixed gap, the same discreteness should modify the propagation of matter fields near the Planck scale; the size of that modification is set by the Barbero-Immirzi parameter, so an independent measurement of $�gamma$ from, say, modified dispersion would be a cross-check against the value fixed by horizon entropy counting.
Because the representation of the holonomy-flux algebra is fixed by diffeomorphism covariance while the Hamiltonian constraint admits many inequivalent regularizations, essentially all predictive content of the theory lives in the choice of constraint. A natural test of the framework is whether a single choice simultaneously yields the correct entropy coefficient, a viable cosmology, and semiclass
The paper's own remark that the diffeomorphism-invariant Hilbert space remains non-separable, because continuous families of higher-valent graphs are not related by smooth diffeomorphisms, bears on state counting; if a separable quotient is the physically correct one, entropy counts and spin-foam amplitudes could shift.
The authors note that the common shorthand 'solutions of the diffeomorphism constraint are diffeomorphism classes of spin networks' is only heuristic, since the averaging map has a nontrivial kernel. Any spin-foam model that treats embedded graphs as abstract combinatorial objects inherits that gap and would need an independent justification.

Original abstract

The goal of this article is to present an introduction to loop quantum gravity -a background independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to providing a bird's eye view of the present status of the subject, the article should also serve as a vehicle to enter the field and explore it in detail. To aid non-experts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory. While the article is essentially self-contained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs. (These can be found in the listed references.) The subject can be approached in different ways. We have chosen one which is deeply rooted in well established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities. In order to keep the article to a reasonable size, and to avoid overwhelming non-experts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,269 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.96 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The goal of this article is to present an introduction to loop quantum gravity -a background independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to providing a bird's eye view of the present status of the subject, the article should also serve as a vehicle to enter the field and explore it in detail. To aid non-experts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory. While the article is essentially self-contained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs. (These can be found in the listed references.) The subject can be approached in different ways. We have chosen one which is deeply rooted in well established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities. In order to keep the article to a reasonable size, and to avoid overwhelming non-experts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The goal of this article is to present an introduction to loop quantum gravity -a background independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry.	contribution 0.92	0.18	0.12	asserted 0.94
s1	Our presentation is pedagogical.	method 0.50	0.42	0.02	asserted 1.00
s2	Thus, in addition to providing a bird's eye view of the present status of the subject, the article should also serve as a vehicle to enter the field and explore it in detail.	contribution 0.79	0.19	0.05	hedged possibility 0.53
s3	To aid non-experts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory.	background 0.54	0.40	0.02	asserted 1.00
s4	While the article is essentially self-contained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs.	limitation 0.78	0.47	0.03	asserted 1.00
s5	(These can be found in the listed references.) The subject can be approached in different ways.	background 0.37	0.24	0.02	asserted 0.74
s6	We have chosen one which is deeply rooted in well established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities.	method 0.93	0.57	0.05	asserted 0.99
s7	In order to keep the article to a reasonable size, and to avoid overwhelming non-experts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.	limitation 1.00	0.72	0.04	asserted 1.00

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 0.61.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1. The figure illustrates a partition

**Figure 2.** FIG. 2. An elementary cell

**Figure 3.** FIG. 3. An elementary cell

**Figure 4.** FIG. 4. Co-ordinatization of the surface phase space

**Figure 5.** FIG. 5. Quantum Horizon. Polymer excitations in the bulk pun

Figures reproduced from arXiv:gr-qc/0404018 by the authors.

References

Works cited (190)

[1]

Creutz M 1983 Quarks, gluons and lattices (Cambridge UP, Cambridge)

View on Pith 1983
[2]

Ashtekar A 1991 Lectures on non-perturbative canonical gravity Notes prepared in collaboration with R. S. Tate (World Scientiﬁc, Singapore)

View on Pith 1991
[3]

Baez J and Muniain J P 1994 Gauge ﬁelds, knots and gravity (World Scientiﬁc, Sin- gapore)

View on Pith 1994
[4]

Gambini R and Pullin J 1996 Loops, knots, gauge theories and quantum gravity (Cam- bridge UP, Cambridge)

View on Pith 1996
[5]

Carlip S 1998 Quantum gravity in 2+1 dimensions (Cambrige UP, Cambridge)

View on Pith 1998
[6]

Rovelli C 1998 Loop quantum gravity Living Rev. Rel 1 1

View on Pith 1998
[7]

Bojowald M. 2001 Quantum Geometry and Symmetry (Saker-Verlag, Aachen)

View on Pith 2001
[8]

Ashtekar A 2002 Quantum geometry and gravity: Recent Adv ances General Relativ- ity and Gravitation ed Bishop N T and Maharaj S D (World Scientiﬁc, Singalore), gr-qc/0112038

View on Pith Pith review arXiv 2002
[9]

Thiemann T 2002 Lectures on loop quantum gravity, to appe ar in Aspects of quantum gravity: From theory to experimental search Lecture Notes in Physics (Springer-Verlag, Berlin 2003), gr-qc/0210094 2004 Modern canonical quantum general relativity , (Cambridge University Press, Cam- bridge, in press), gr-qc/0110034

View on Pith Pith review arXiv 2002
[10]

Perez A 2003 Spin foam models for quantum gravity Class. Quant. Grav. 20 R43–R104

View on Pith 2003
[11]

C. Rovelli 2004 Quantum Gravity (Cambridge University Press, Cambridge, in press) Classical theory:

View on Pith 2004
[12]

Ashtekar A 1986 New variables for classical and quantum gravity Phys. Rev. Lett. 57 2244–2247

View on Pith 1986
[13]

Ashtekar A (1987) New Hamiltonian formulation of gener al relativity Phys. Rev. D36 1587–1602

View on Pith 1987
[14]

Samuel J 1987 A Lagrangian basis for Ashtekar’s reformu lation of canonical gravity Pramana-J. Phys. 24 28 L429-L432 Jacobson T and Smolin L 1987 The left handed spin connection a s a variable for canonical greavity Phys. Lett. B196 39-42

View on Pith 1987
[15]

Ashtekar A, Mazur P and Torre C G 1987 BRST structure of ge neral relativity in terms of new variables Phys. Rev D36 2955-2962

View on Pith 1987
[16]

Ashtekar A, Romano J D and Tate R S 1989 New variables for g ravity: Inclusion of matter Phys. Rev. D40 2572–2587

View on Pith 1989
[17]

Jacobson T 1988 New variables for canonical supergravi ty, Class. Quant. Grav. 5 923– 935 Matschull H J and Nicolai H 1994 Canonical Quantum Supergrav ity in three- dimensions Nucl. Phys. B411 609–646

View on Pith 1988
[18]

Ashtekar A, Balachandran A P and Jo S 1989 The CP problem i n quantum gravity, Int. J. Mod. Phys. A4 1493—1514

View on Pith 1989
[19]

Pleba´ nski J F 1977 On the separation of Einsteinian sub structures J. Math. Phys. 18 2511 115

View on Pith 1977
[20]

Capovilla R, Dell J and Jacobson T 1989 General relativi ty without a metric Phys. Rev. Lett. 63 2325–2328 Capovilla R, Dell J, Jacobson T and Mason L 1991 Selfdual two f orms and gravity Class. Quant. Grav. 8 41–57

View on Pith 1989
[21]

Holst S 1996 Barbero’s Hamiltonian derived from a gener alized Hilbert-Palatini action Phys. Rev. D53 5966-5969 Wisniewski J 2001 Symplectic structure from Holst action, p re-print

View on Pith 1996
[22]

Samuel J 2000 Is Barbero’s Hamiltonian formulation a ga uge theory of Lorentzian gravity? Class. Quant. Grav. 17 L141-L148

View on Pith 2000
[23]

Robinson D C 1995 A Lagrangian formalism for the Einstei n-Yang-Mills equations J. Math. Phys. 36 3733-42 Lewandowski J, Okol’ow A 2000 2-Form Gravity of the Lorentzi an Signature Class. Quant. Grav. 17 L47-L51

View on Pith 1995
[24]

Alexandrov S, Livine E R 2003 SU(2) Loop Quantum Gravity seen from Covariant Theory Phys. Rev. D67 044009

View on Pith 2003
[25]

Freidel L and Krasnov K 1999 BF description of higher dim ensional gravity theories Adv. Theor. Math. Phys. 3 1289–1324

View on Pith 1999
[26]

Jacobson T, Romano J D 1992 Degenerate Extensions Of Gen eral Relativity Class. Quant. Grav. 9 L119–L124

View on Pith 1992
[27]

Matschull H J 1996 Causal structure and diﬀeomorphisms in Ashtekar’s gravity Class. Quant. Grav. 13 765–782

View on Pith 1996
[28]

Jacobson T 1996 (1+1) sector of (3+1) gravity Class. Quant. Grav. 13 L111–L116, Erratum-ibid. 1996 Class. Quant. Grav. 13 3269

View on Pith 1996
[29]

Lewandowski J and Wisniewski J 1997 (2+1) sector of (3+1 ) gravity Class. Quant. Grav. 14 775–782

View on Pith 1997
[30]

Lewandowski J and Wisniewski J 1999 Degenerate sectors of the Ashtekar gravity Class. Quant. Grav. 16 3057–3069

View on Pith 1999
[31]

Penrose R 1976 Non-linear graviton and curved twistor t heory Gen. Rel.& Grav. 7 31-52

View on Pith 1976
[32]

Ko M, Ludvigsen M, Newman E T and Tod P 1981 The theory of H space Phys. Rep. 71 51–139 Connections and loops:

View on Pith 1981
[33]

Rovelli C and Smolin L 1988 Knot theory and quantum gravi ty Phys. Rev. Lett. 61 1155-1158

View on Pith 1988
[34]

Rovelli C and Smolin L 1990 Loop representation for quan tum general relativity Nucl. Phys. B331 80–152

View on Pith 1990
[35]

Ashtekar A, Husain V, Rovelli C, Samuel J, and Smolin L 19 89 2+1 quantum gravity as a toy model for the 3+1 theory Class. Quant. Grav. 6 L185–L193

View on Pith
[36]

Ashtekar A, Rovelli C, and Smolin L 1991 Gravitons and lo ops Phys. Rev. D44 1740– 1755

View on Pith 1991
[37]

Smolin L 1992 Recent developments in non-perturbative quantum gravity Quantum Gravity and Csomology ed Mercader J, Sol´ a J and Verdaguer R (World Scientiﬁc, Singapore)

View on Pith 1992
[38]

Goldberg J N, Lewandowski J, Stornaiolo C 1992 Degenera cy in loop variables Com- 116 mun. Math. Phys. 148 377–402 Background independent quantization of theories of connec tions:

View on Pith 1992
[39]

Ashtekar A and Isham C J 1992 Representation of the holon omy algebras of gravity and non-Abelian gauge theories Class. Quant. Grav. 9 1433–1467

View on Pith 1992
[40]

Ashtekar A and Lewandowski J 1994 Representation theor y of analytic holonomy al- gebras, in Knots and Quantum Gravity ed Baez J C (Oxford U. Press, Oxford)

View on Pith 1994
[41]

Baez J C 1994 Generalized measures in gauge theory Lett. Math. Phys. 31 213–223

View on Pith 1994
[42]

Lewandowski J 1994 Topological Measure and Graph-Diﬀe rential Geometry on the Quotient Space of Connections Int. J. Mod. Phys. D3 207–210

View on Pith 1994
[43]

Ashtekar A, Lewandowski L, Marolf D, Mour˜ ao J and Thiem ann T 1995 A manifestly gauge invariant approach to quantum gauge theories, in Geometry of Constrained Dy- namical Systems ed Charap J M (Cambridge U. Press, Cambridge)60–72

View on Pith 1995
[44]

Marolf D and Mour˜ ao J 1995 On the support of the Ashtekar -Lewandowski measure Commun. Math. Phys. 170 583-606

View on Pith 1995
[45]

Ashtekar A and Lewandowski J 1995 Projective technique s and functional integration Jour. Math. Phys. 36 2170–2191

View on Pith 1995
[46]

Ashtekar A, Lewandowski L, Marolf D, Mour˜ ao J and Thiem ann T 1996 Coherent State Transforms for Spaces of Connections Jour. Funct. Analysis 135 519-551

View on Pith 1996
[47]

Baez J C and Sawin S 1997 Functional integration on space s of connections Jour. Funct. Analysis 150 1–27

View on Pith 1997
[48]

Ashtekar A, Corichi A and Zapata J A 1998 Quantum theory o f geometry: III. Non- commutativity of Riemannian structures Class. Quant. Grav. 15 2955–2972

View on Pith 1998
[49]

Marolf D, Mour˜ ao J, Thiemann T 1997 The Status of Diﬀeom orphism Superselection in Euclidean 2+1 Gravity J. Math. Phys. 38 4730-4740

View on Pith 1997
[50]

Mour˜ ao J M, Thiemann T, Velhinho J M 1999 Physical Prope rties of Quantum Field Theory Measures J. Math. Phys. 40 2337–2353

View on Pith 1999
[51]

Velhinho J M 2002 A groupoid approach to spaces of genera lized connections J. Geom. Phys. 41 166–180

View on Pith 2002
[52]

Fleischhack C 2000 Stratiﬁcation of the Generalized Ga uge Orbit Space Commun. Math. Phys. 214 607–649

View on Pith 2000
[53]

Fleischhack C 2003 On the Gribov Problem for Generalize d Connections Commun. Math. Phys. 234 423–454

View on Pith 2003
[54]

Fleischhack C 2003 Hyphs and the Ashtekar-Lewandowski Measure J. Geom. Phys. 45 231–251

View on Pith 2003
[55]

Sahlmann H 2002 When Do Measures on the Space of Connecti ons Support the Triad Operators of Loop Quantum Gravity? Preprint gr-qc/0207112 Sahlmann H 2002 Some Comments on the Representation Theory o f the Algebra Un- derlying Loop Quantum Gravity Preprint gr-qc/0207111

View on Pith Pith review arXiv 2002
[56]

Oko l´ ow A, Lewandowski J 2003 Diﬀeomorphism covariant represen tations of the holonomy-ﬂux star-algebra Class. Quant. Grav. 20 3543–3568

View on Pith 2003
[57]

Sahlmann H and Thiemann T 2003 On the superselection the ory of the Weyl algebra for diﬀeomorphism invariant quantum gauge theories Preprint gr-qc/0302090 Sahlmann H and Thiemann T 2003 Irreducibility of the Ashteka r-Isham-Lewandowski representation Preprint gr-qc/0303074 117

View on Pith Pith review arXiv 2003
[58]

Lewandowski J, Oko l´ ow A, Sahlmann H, Thiemann T 2003 Uniqueness of the diﬀeo- morphism invariant state on the quantum holonomy-ﬂux algeb ra Preprint Spin networks:

View on Pith 2003
[59]

Penrose R 1971 Angular momentum: an approach to combina torial space-time Quan- tum Theory and Beyond ed Bastin T (Cambridge University Press)

View on Pith 1971
[60]

Rovelli C and Smolin L 1995 Spin networks and quantum gra vity Phys. Rev. D52 5743–5759

View on Pith 1995
[61]

Baez J C 1996 Spin networks in non-perturbative quantum gravity, in The Interface of Knots and Physics ed Kauﬀman L (American Mathematical Society, Providence) pp. 167–203 Baez J C 1996 Spin networks in gauge theory Adv. Math.117 253–272

View on Pith 1996
[62]

Thiemann T 1998 The inverse loop transform J. Math. Phys. 39 1236–1248

View on Pith 1998
[63]

Baez J C and Sawin S 1998 Diﬀeomorphism–invariant spin n etwork states Jour. Funct. Analysis 158 253–266

View on Pith 1998
[64]

C Fleischhack 2003 Proof of a Conjecture by Lewandowski and Thiemann Preprint math-ph/0304002 Geometric operators and their properties

View on Pith Pith review arXiv 2003
[65]

Rovelli C and Smolin L 1995 Discreteness of area and volu me in quantum gravity Nucl. Phys. B442 593–622; Erratum: Nucl. Phys. B456 753

View on Pith 1995
[66]

Ashtekar A and Lewandowski L 1995 Diﬀerential geometry on the space of connections using projective techniques Jour. Geo. & Phys. 17 191–230

View on Pith 1995
[67]

Loll R 1995 The volume operator in discretized quantum g ravity Phys. Rev. Lett. 75 3048–3051

View on Pith 1995
[68]

Loll R 1995 Spectrum of the Volume Operator in Quantum Gr avity Nucl. Phys. B460 143–154

View on Pith 1995
[69]

Frittelli S, Lehner L and Rovelli C 1996 Class. Quant. Grav. 13 2921–2932

View on Pith 1996
[70]

De Pietri R, Rovelli C 1996 Phys. Rev. D54 2664–2690

View on Pith 1996
[71]

Lewandowski J. 1997 Volume and Quantizations Class. Quant. Grav. 14 71–76

View on Pith 1997
[72]

Ashtekar A and Lewandowski J 1997 Quantum theory of geom etry I: Area operators Class. Quant. Grav. 14 A55–A81

View on Pith 1997
[73]

Ashtekar A and Lewandowski J 1997 Quantum theory of geom etry II: Volume Opera- tors Adv. Theo. Math. Phys. 1 388–429

View on Pith 1997
[74]

Loll R 1997 Simplifying the spectral analysis of the vol ume operator Nucl. Phys. B500 405–420

View on Pith 1997
[75]

Loll R 1997 Further results on geometric operators in qu antum gravity Class. Quant. Grav. 14 1725–1741

View on Pith 1997
[76]

De Pietri R 1997 Spin Networks and Recoupling in Loop Qua ntum Gravity Nucl. Phys. Suppl 57 251-254

View on Pith 1997
[77]

De Pietri R 1997 On the relation between the connection a nd the loop representation of quantum gravity Class. Quant. Grav. 14 53–70

View on Pith 1997
[78]

Thiemann T 1998 Closed formula for the matrix elements o f the volume operator in canonical quantum gravity J. Math. Phys. 39 3347-3371

View on Pith 1998
[79]

Thiemann T 1998 A length operator for canonical quantum gravity Jour. Math. Phys. 118 39 3372–3392

View on Pith 1998
[80]

Major S A 1999 Operators for quantized directions Class. Quant. Grav. 16 3859-3877 Barbero-Immirzi ambiguity

View on Pith 1999
[81]

Barbero F 1996 Real Ashtekar variables for Lorentzian s ignature space-times Phys. Rev. D51 5507–5510

View on Pith 1996
[82]

Immirzi G 1997 Quantum gravity and Regge calculus Nucl. Phys. Proc. Suppl. 57 65–72

View on Pith 1997
[83]

Rovelli C. and Thiemann T. (1998) The Immirizi paramete r in quantum general rela- tivity Phys. Rev. D57 1009–1014

View on Pith 1998
[84]

Gambini R, Obregon O and Pullin J 1999 Yang-Mills analog s of the Immirzi ambiguity Phys. Rev. D59 047505 Quantum Einstein’s equation I

View on Pith 1999
[85]

Kuchaˇ r K 1993 Canonical Quantum Gravity General Relativity and Gravitation 1992 ed Gleiser R J, Kozameh C N, Moreschi O M (Institute of Physics Publishing) 119–150

View on Pith 1993
[86]

Ashtekar A, Tate R S and Uggla C 1993 Minisuperspaces: Ob servables and quantiza- tion Int. J. Phys. D2 15–50 Ashtekar A, Tate R S and Uggla C 1993 Minisuperspaces: Symmet ries and quantiza- tion Misner Festschrift ed Hu B L et al (Cambridge U. P., Cambridge)

View on Pith 1993
[87]

Ashtekar A and Tate R S 1994 An algebraic extension of Dir ac quantization: Examples Jour. Math. Phys. 35 6434–6470

View on Pith 1994
[88]

Marolf D 1995 Reﬁned algebraic quantization: Systems w ith a single constraint Preprint gr-qc/9508015

View on Pith Pith review arXiv 1995
[89]

Ashtekar A, Lewandowski J, Marolf D, Mour˜ ao J and Thiem ann T 1995 Quantization of diﬀeomorphism invariant theories of connections with lo cal degrees of freedom Jour. Math. Phys. 36 6456–6493

View on Pith 1995
[90]

Marolf D, Mour˜ ao J and Thiemann T 1997 The status of diﬀe omorphism super- selection in Euclidean 2+1 gravity J. Math. Phys. 38 4730-4740

View on Pith 1997
[91]

Guilini N and Marolf D 1999 On the Generality of Reﬁned Al gebraic Quantization Class. Quant. Grav. 16 2479–2488 A uniqueness theorem for constraint quantization Class. Quant. Grav. 16 2489–2505

View on Pith 1999
[92]

Lewandowski J and Thiemann T 1999 Diﬀeomorphism invari ant quantum ﬁeld theories of connections in terms of webs Class. Quant. Grav. 16 2299–2322

View on Pith 1999
[93]

Corichi A and Zapata J A 1997 On diﬀeomorphism invarianc e for lattice theories Nucl. Phys. B493 475–490 Quantum Einstein’s equation II

View on Pith 1997
[94]

Rovelli C and Smolin L 1994 The physical Hamiltonian in n onperturbative quantum gravity Phys. Rev. Lett. 72 446–449

View on Pith 1994
[95]

Thiemann T 1996 Anomaly-free formulation of non-pertu rbative, four-dimensional Lorentzian quantum gravity Phys. Lett. B380 257–264

View on Pith 1996
[96]

Thiemann T 1998 Quantum spin dynamics (QSD) Class. Quant. Grav. 15 839–873

View on Pith 1998
[97]

Thiemann T. 1998 QSD III: Quantum constraint algebra an d physical scalar product in quantum general relativity Class. Quant. Grav. 15 1207–1247 119

View on Pith 1998
[98]

Thiemann T 1998 QSD V: Quantum gravity as the natural reg ulator of matter quantum ﬁeld theories Class. Quant. Grav. 15 1281–1314

View on Pith 1998
[99]

Thiemann T 2001 Quantum Spin Dynamics (QSD) : VII. Sympl ectic Structures and Continuum Lattice Formulations of Gauge Field Theories Class. Quant. Grav. 18 3293– 3338

View on Pith 2001
[100]

Gambini R, Lewandowski J, Marolf D and Pullin J 1998 On t he consistency of the constraint algebra in spin network quantum gravity Int. J. Mod. Phys. D7 97–109

View on Pith 1998
[101]

Lewandowski J and Marolf D 1998 Loop constraints: A hab itat and their algebra Int. J. Mod. Phys. D7 299–330

View on Pith 1998
[102]

Gaul G and Rovelli C 2001 Generalized hamiltonian cons traint operator in loop quan- tum gravity and its simplest Euclidean matrix elements Class. Quant. Grav. 18 1593– 1624 Big-bang:

View on Pith 2001
[103]

Kodama H 1988 Specialization of Ashtekar’s formalism to Bianchi cosmology Prog. Theor. Phys. 80 1024–1040 Kodama H 1990 Holomorphic wavefunction of the universe Phys. Rev. D42 2548–2565

View on Pith 1988
[104]

Bojowald M 2001 Absence of singularity in loop quantum cosmology Phys. Rev. Lett. 86 5227–5230

View on Pith 2001
[105]

Bojowald M 2001 Inverse scale factor in isotropic quan tum geometry Phys. Rev. D64 084018

View on Pith 2001
[106]

Bojowald M 2001 Dynamical initial conditions in quant um cosmology Phys. Rev. Lett. 87 121301

View on Pith 2001
[107]

Bojowald M 2001 Loop Quantum Cosmology IV: Discrete Ti me Evolution Class. Quant. Grav. 18 1071–1088

View on Pith 2001
[108]

Bojowald M 2001 Loop quantum cosmology III: Wheeler-D eWitt operators Class. Quant. Grav. 18 1055–1070 Bojowald M 2002 The Semiclassical Limit of Loop Quantum Cosm ology Class. Quant. Grav. 18 L109–L116

View on Pith 2001
[109]

Bojowald M 2001 The Inverse Scale Factor in Isotropic Q uantum Geometry Phys.Rev. D64 084018

View on Pith 2001
[110]

Bojowald M 2002 Isotropic Loop Quantum Cosmology Class.Quant.Grav. 19 2717– 2742

View on Pith 2002
[111]

Bojowald M, Hinterleitner F 2002 Isotropic Loop Quant um Cosmology with Matter Phys.Rev. D66 104003

View on Pith 2002
[112]

Bojowald M and Vandersloot K 2003 Loop Quantum Cosmolo gy, Boundary Proposals, and Inﬂation Phys.Rev. D67 124023

View on Pith 2003
[113]

Bojowald M 2003 Homogeneous Loop Quantum Cosmology Class.Quant.Grav. 20 2595–2615

View on Pith 2003
[114]

Bojowald M 2003 Initial Conditions for a Universe Gen. Rel. Grav. 35, 1877-1883 (First Prize in the Gravity Research Foundation Essay Conte st)

View on Pith 2003
[115]

Ashtekar A, Bojowald M, Lewandowski J 2003 Mathematic al structure of loop quantum cosmology Adv. Theor. Math. Phys. 7 233–268

View on Pith 2003
[116]

Bojowald M, Date G and Vandersloot K 2004 Homogeneous L oop Quantum Cosmol- ogy: The Role of the Spin Connection Class. Quant. Grav. textbf21 1253-1278 120

View on Pith 2004
[117]

Ashtekar A, Bojowald M and Willis J 2004 Quantum correc tions to Friedmann equa- tions in loop quantum cosmology (in preparation) Black holes:

View on Pith 2004
[118]

Bekenstein J D 1973 Black holes and entropy Phys. Rev. D7 2333–2346 (1974) Generalized second law of thermodynamics in black ho le physics Phys. Rev. D9 3292–3300 Bekenstein J D and Meisels A 1977 Einstein A and B coeﬃcients f or a black hole Phys. Rev. D15 2775–2781

View on Pith 1974
[119]

Bardeen J W, Carter B and Hawking S W 1973 The four laws of black hole mechanics Commun. Math. Phys. 31 161-170

View on Pith 1973
[120]

Hawking S W 1975 Particle creation by black holes Commun. Math. Phys. 43 199–220

View on Pith 1975
[121]

Gibbons G and Hawking S W 1977 Cosmological event horiz ons, thermodynamics, and particle creation Phys. Rev. D15 2738–2751

View on Pith 1977
[122]

Smolin L 1995 Linking topological quantum ﬁeld theory and nonperturbative quantum gravity J. Math. Phys. 36 6417–6455

View on Pith 1995
[123]

Barreira M, Carfora M and Rovelli C 1996 Physics with no n-perturbative quantum gravity: radiation from a quantum black hole Gen. Rel. Grav. 28 1293–1299 Rovelli C 1996 Black hole entropy from loop quantum gravity Phys. Rev. Lett. 14 3288–3291 Rovelli C 1996 Loop quantum gravity and black hole physics Helv. Phys. Acta. 69 582–611

View on Pith 1996
[124]

Krasnov K 1997 Geometrical entropy from loop quantum g ravity Phys. Rev. D55 3505–3513 Krasnov K 1998 On statistical mechanics of Schwarzschild bl ack holes Gen. Rel. Grav. 30 53–68

View on Pith 1997
[125]

Jacobson T, Kang G and Myers R C 1994 On black hole entrop y Phys. Rev. D49 6587–6598

View on Pith 1994
[126]

Wald R. (1993) Black hole entropy is Noether charge Phys. Rev. D48 3427–3431 Iyer V and Wald R 1994 Some properties of Noether charge and a p roposal for dynam- ical black hole entropy Phys. Rev. D50 846–864

View on Pith 1993
[127]

Ashtekar A, Baez J C, Corichi A, and Krasnov K 1998 Quant um geometry and black hole entropy (1998) Phys. Rev. Lett. 80 904–907

View on Pith 1998
[128]

Ashtekar A, Corichi A and Krasnov K 1999 Isolated horiz ons: the classical phase space Adv. Theor. Math. Phys. 3 418–471

View on Pith 1999
[129]

Ashtekar A, Baez J C and Krasnov K 2000 Quantum geometry of isolated horizons and black hole entropy Adv. Theo. Math. Phys. 4 1–95

View on Pith 2000
[130]

Kaul R K and Majumdar P 2000 Logarithmic corrections to the Bekenstein-Hawking entropy Phys. Rev. Lett. 84 5255–5257

View on Pith 2000
[131]

Ashtekar A, Beetle C and Fairhurst S 1999 Isolated hori zons: a generalization of black hole mechanics Class. Quantum Grav. 16 L1–L7 Ashtekar A, Beetle C and Fairhurst S 2000 Mechanics of isolat ed horizons Class. Quan- tum Grav. 17 253–298

View on Pith 1999
[132]

Lewandowski J 2000 Space-times admitting isolated ho rizons Class. Quantum Grav. 17 L53–L59 121

View on Pith 2000
[133]

Ashtekar A, Fairhurst S and Krishnan B 2000 Isolated Ho rizons: Hamiltonian Evolu- tion and the First Law Phys. Rev. D62 104025

View on Pith 2000
[134]

Ashtekar A, Beetle C and Lewandowski J 2001 Mechanics o f rotating isolated horizons Phy. Rev. D64 044016

View on Pith 2001
[135]

Ashtekar A, Beetle C and Lewandowski J 2002 Geometry of generic isolated horizons Class. Quantum Grav. 19 1195–1225

View on Pith 2002
[136]

Ashtekar A, Corichi A and Sudarski D 2003 Non-Minimall y Coupled Scalar Fields and Isolated Horizons Class. Quantum Grav. 20 3413-3425

View on Pith 2003
[137]

Ashtekar A and Corichi A 2003 Non-minimal couplings, q uantum geometry and black hole entropy 20 Class. Quantum Grav. 20 4473-4484

View on Pith 2003
[138]

Ashtekar A, Engle J, Pawlowski, T and van der Broeck C 20 04 Multipole moments of isolated horizons Class. Quant. Grav. 21 2549-2570

View on Pith
[139]

Ashtekar A 2003 Black hole entropy: Inclusion of disto rtion and angular momentum, http://www.phys.psu.edu/events/index.html?event id=517&event type=17 Ashtekar A, Engle J and van der Broeck C 2004 (in preparation)

View on Pith 2003
[140]

Wheeler J A 1992 It from bit Sakharov Memorial Lectures on Physics, Vol 2 ed Keldysh L and Feinberg V (Nova Science, Moscow)

View on Pith 1992
[141]

Ghosh A and Mitra P 2004 A bound on the log correction to t he black hole area law pre-print gr-qc/0401070 Low energy physics:

View on Pith Pith review arXiv 2004
[142]

Ashtekar A, Rovelli C and Smolin L 1992 Weaving a classi cal geometry with quantum threads Phy. Rev. Lett. 69 237–240

View on Pith 1992
[143]

Arnsdorf M, Gupta S 2000 Loop quantum gravity on non-co mpact spaces Nucl. Phys. B577 529-546

View on Pith 2000
[144]

Corichi A, Reyes J M 2001 A Gaussian Weave for Kinematic al Loop Quantum Gravity Int. J. Mod. Phys. D10 325-338

View on Pith 2001
[145]

Hall B C 1994 The Segal-Bergmann coherent state transf orm for compact Lie Lie groups J. Funct. Anal. 122 103-151

View on Pith 1994
[146]

Sahlmann H, Thiemann T and Winkler O 2001 Coherent stat es for canonical quantum general relativity and the inﬁnite tensor product extensio n Nucl. Phys. B606 401-440

View on Pith 2001
[147]

Thiemann T 2001 Gauge ﬁeld theory coherent states (GCS ): I. general properties Class. Quant. Grav. 18 2025-2064 T. Thiemann, O. Winkler 2001 Gauge Field Theory Coherent Sta tes (GCS) : II. Peakedness Properties Class. Quant. Grav. 18 2561–2636 Thiemann T, Winkler O 2001 Gauge Field Theory Coherent State s (GCS) : III. Ehren- fest Theorems Class. Quant. G...

View on Pith 2001
[148]

Hanno Sahlmann, Thomas Thiemann 2002 Towards the QFT o n Curved Spacetime Limit of QGR. I: A General Scheme Preprint gr-qc/0207030 Sahlmann H Thomas Thiemann 2002 Towards the QFT on Curved Spa cetime Limit of QGR. II: A Concrete Implementation Preprint gr-qc/0207031

View on Pith Pith review arXiv 2002
[149]

Thiemann T 2002 Complexiﬁer Coherent States for Quant um General Relativity Preprint gr-qc/0206037 122

View on Pith Pith review arXiv 2002
[150]

Bombelli L 2002 Statistical geometry of random weave s tates Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity ed Gurzadyan VG, Jantzen RT, and Ruﬃni R (World Scientiﬁc, Singapore) gr-qc/0101080

View on Pith Pith review arXiv 2002
[151]

Ashtekar A and Isham C J 1992 Phys. Lett. B274 393-398

View on Pith 1992
[152]

Varadarajan M 2000 Fock representations from U(1) hol onomy algebras Phys. Rev. D61 104001 Varadarajan M. (2001) M. Photons from quantized electric ﬂu x representations Phys. Rev. D64 104003

View on Pith 2001
[153]

Ashtekar A and Lewandowski J 2001 Relation between pol ymer and Fock excitations Class. Quant. Grav. 18 L117–L127

View on Pith 2001
[154]

Velhinho J M 2002 Invariance properties of induced Foc k measures for U(1) holonomies Commun. Math. Phys. 227 541–550

View on Pith 2002
[155]

Ashtekar A, Fairhurst S and Willis J 2003 Quantum gravi ty, shadow states, and quan- tum mechanics Class. Quantum Grav. 20, 1031-1061

View on Pith 2003
[156]

Ashtekar A, Fairhurst S and Ghosh A 2004 (in preparatio n)

View on Pith 2004
[157]

Varadarajan M. 2002 Gravitons from a loop representat ion of linearised gravity Phys. Rev. D66 024017

View on Pith 2002
[158]

Ashtekar A, Ghosh A and Van Den Broeck C 2004 (in prepara tion)

View on Pith 2004
[159]

Bobienski M, Lewandowski J, Mroczek M 2002 A 2-Surface Quantization of the Lorentzian Gravity Proceedings of the Ninth Marcel Grossmann Meeting on Genera l Relativity ed Gurzadyan VG, Jantzen RT, and Ruﬃni R (World Scientiﬁc, Si ngapore) gr-qc/0101069

View on Pith Pith review arXiv 2002
[160]

Ashtekar A, Lewandowski J and Sahlmann H 2003 Polymer a nd Fock representations of a scalar ﬁeld Class. Quant. Grav. 20 L11–L21 Spin foams and ﬁniteness:

View on Pith 2003
[161]

Baez J C 2000 An introduction to spin foam models of quan tum gravity and BF theory Lect. Notes Phys. 543 25–94

View on Pith 2000
[162]

Baez J C 1998 Spin foam models Class. Quant. Grav. 15 1827–1858

View on Pith 1998
[163]

Reisenberger M P 1997 A lattice worldsheet sum for Reis enberger M P 1997 4-d Eu- clidean general relativity Preprint gr-qc/9711052 Reisenberger M P 1999 On relativistic spin network vertices J. Math. Phys. 40 2046– 2054

View on Pith Pith review arXiv 1997
[164]

Reisenberger M P and Rovelli C 2001 Spacetime as a Feynm an diagram: the connection formulation Class. Quant. Grav. 18 121–140 Reisenberger M P and Rovelli 2002 Spacetime states and covar iant quantum theory Phys. Rev. D65 125016

View on Pith 2001
[165]

Barrett J W and Crane L 1998 Relativistic spin networks and quantum gravity J. Math. Phys. 39 3296–3302 Barrett J W and Crane L 2000 A Lorentzian signature model for q uantum general relativity Class. Quant. Grav. 17 3101–3118

View on Pith 1998
[166]

Perez A 2001 Finiteness of a spinfoam model for Euclide an quantum general relativity Nucl. Phys. B599 427–434 Perez A and Rovelli C 2001 Spin foam model for Lorentzian gene ral relativity Phys. Rev. D63 041501 123 Crane L, Perez A and Rovelli C 2001 Perturbative ﬁniteness in spin-foam quantum gravity Phys. Rev. Lett. 87 181301 Crane L, Perez A and Rovell...

View on Pith 2001
[167]

Baez J, Christensen D, Halford T R, Tsang DC 2002 Spin Fo am Models of Riemannian Quantum Gravity Class. Quant. Grav. 194627-4648

View on Pith 2002
[168]

Gambini R and Pullin J 2002 A ﬁnite spin-foam-based the ory of three and four dimen- sional quantum gravity Phys. Rev. D66 024020

View on Pith 2002
[169]

Lauscher O and Reuter M 2002 Is quantum Einstein gravit y non-perturbatively renor- malizable? Class. Quant. Grav. 19 483–492

View on Pith 2002
[170]

Percacci R and Perini D 2003 Asymptotic safety of gravi ty coupled to matter Phys. Rev. D68044018 Perini D 2003 Gravity and matter with asymptotic safety pre-print hep-th/0305053

View on Pith Pith review arXiv 2003
[171]

Bojowald M and Perez A 2003 Spin foam quantization and a nomalies gr-qc/0303026

View on Pith Pith review arXiv 2003
[172]

Freidel L and Louapre D 2003 Diﬀeomorphisms and spin fo am models, Nucl.Phys. B662 279-298 Freidel L and Louapre D 2003 Non-perturbative summation ove r 3D discrete topologies Phys. Rev. D68 104004 hep-th/0211026

View on Pith Pith review arXiv 2003
[173]

Perez A and Noui K 2004 Three dimensional loop quantum g ravity: coupling to point particles pre-print gr-qc/0402111 2004 Three dimensional loop quantum gravity: physical scal ar product and spin foam models pre-print gr-qc/0402110 Outlook:

View on Pith Pith review arXiv 2004
[174]

Ashtekar A, Lewandowski J, Marolf D, Mour˜ ao J and Thiemann T 1997 SU(N) Quan- tum Yang-Mills theory in two dimensions: A complete solutio n J. Math. Phys. 38, 5453-5482

View on Pith 1997
[175]

Ashtekar A and Sahlmann H 2004 (in preparation)

View on Pith 2004
[176]

Okolw A 204 Representations of quantum geometry Ph.D. thesis, University of Warsaw

View on Pith
[177]

Rovelli C and Speziale S 2003 Reconcile Planck-scale d iscreteness and the Lorentz- Fitzgerald contraction Phys. Rev. D67 064019

View on Pith 2003
[178]

Thiemann T 2003 The Phoenix project: Master constrain t programme for loop quan- tum gravity Preprint gr-qc/0305080

View on Pith Pith review arXiv 2003
[179]

Dittrich B 2004 Testing the master constraint program me for loop quantum gravity http://www.phys.psu.edu/events/index.html?event id=850&event type=17

View on Pith 2004
[180]

Klauder J 2003 Aﬃne quantum gravity Int. J. Mod. Phys. D12 1769-1774 2004 The utility of coherent states and other mathematical m ethods in the foundations of aﬃne quantum gravity, pre-print hep-th/0401214

View on Pith Pith review arXiv 2003
[181]

Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Consi stent canonical quantiza- tion of general relativity in the space of Vassiliev knot inv ariants Phys. Rev. Lett. 84 2314–2317 2000 Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical struc- ture Class. Quant. Grav. 17 3211-3238 2000 Canonical quantum gravity in the Vassiliev...

View on Pith 2000
[182]

Gambini R and Pullin J 2003 Canonical quantization of g eneral relativity in discrete space-times Phys. Rev. Lett. 90 021301 Gambini R, Porto R and Pullin J 2004 Loss of coherence from dis crete quantum gravity Class. Quant. Grav. 21 L51-L57 Gambini R, Porto R and Pullin J 2004 A relational solution to t he problem of time in quantum mechanics and quantum...

View on Pith Pith review arXiv 2003
[183]

Horowitz G. T. 1998 Quantum states of black holes, in Black Holes and Relativistic Stars, ed Wald R M ( University of Chicago Press, Chicago)

View on Pith 1998
[184]

Carlip S 1999 Entropy from Conformal Field Theory at Ki lling Horizons Class. Quant. Grav. 16 3327–3348

View on Pith 1999
[185]

Dreyer O, Ghosh A and Wisniewski J 2001 Black hole entro py calculations based on symmetries, Class. Quant. Grav. 18 1929-1938

View on Pith 2001
[186]

Carlip S 2002 Near-Horizon Conformal Symmetry and Bla ck Hole Entropy Phys. Rev. Lett. 88 241301

View on Pith 2002
[187]

Ashtekar A, Krishnan B 2002 Dynamical Horizons: Energ y, Angular Momentum, Fluxes and Balance Laws, Phys. Rev. Lett. 89 261101 2003 Dynamical horizons and their properties, Phys. Rev. D68 104030

View on Pith 2002
[188]

Bojowald M 2002 Inﬂation from Quantum Geometry Phys.Rev.Lett. 89 261301

View on Pith 2002
[189]

Bojowald M and Date G 2004 Quantum suppression of the ge neric chaotic behavior close to cosmological singularities Phys. Rev. Lett. 92 071302

View on Pith 2004
[190]

Tsujikawa S, Singh P and Maartens R 2003 Loop quantum gr avity eﬀects on inﬂation and the CMB, pre-print astro-ph/0311015 125

View on Pith Pith review arXiv 2003

Forward citations

Showing 60 of 101 Pith papers that cite this

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. See all 101 Pith citations

Infrared-Finite Positivity Bounds in 4D Gravity
hep-th 2026-10 conditional novelty 8.0 of 10

An infrared-finite positivity bound on four-scalar Wilson coefficients in 4D gravity is derived using half-space scattering and a geometric cure for the infrared divergence.
One Method to Find Them All: Analytic Black Holes beyond Einstein
gr-qc 2026-10 accept novelty 7.0 of 10

Closed-form Kerr deformations are constructed for six higher-curvature interactions at generic spin, using a common generating kernel without mode decomposition or slow-rotation expansion.
Analytic Metric for Rotating Black Holes in Higher-Derivative Gravity
gr-qc 2026-10 conditional novelty 7.0 of 10

A new analytic construction yields the deformed metric of a rapidly spinning black hole in parity-even cubic gravity at first order in the coupling, without slow-rotation or weak-field expansions.
Constraining quantum-gravity predictions for evolving dark energy
astro-ph.CO 2026-09 unverdicted novelty 7.0 of 10

Group field theory quantum gravity predicts dark energy equations of state that are constrained by BAO and supernova data, with the logarithmic branch resembling a cosmological constant and oscillatory solutions allow...
A matrix free action of the Ashtekar-Lewandowski volume operator of loop quantum gravity
gr-qc 2026-06 unverdicted novelty 7.0 of 10

Develops a matrix-free SRQ-based action for the AL volume operator that exactly preserves the kernel and supports large-scale Monte Carlo and spectral estimates without dense matrices.

Show 55 more citing papers

Homogeneous cosmologies as group field theory condensates
gr-qc 2013-11 conditional novelty 7.0 of 10

Group field theory condensate states, required to approximately solve the quantum equations of motion, yield an effective cosmological equation that reduces to the Friedmann equation in a semiclassical limit.
Post-Newtonian, Quasi-Circular Binary Inspirals in Quadratic Modified Gravity
gr-qc 2011-10 conditional novelty 7.0 of 10

Scalar radiation from black-hole binaries in quadratic modified gravity enters at -1PN and 2PN orders, providing a template for gravitational-wave constraints on the theory.
A New Spin Foam Model for 4d Gravity
gr-qc 2007-08 conditional novelty 7.0 of 10

A new spin foam vertex is constructed that solders neighbouring tetrahedra, is argued to quantize the gravitational rather than the topological sector of Plebanski gravity, and admits a quantized Immirzi parameter.
Loop quantum cosmology of k=1 FRW models
gr-qc 2006-12 conditional novelty 7.0 of 10

In loop quantum cosmology the closed k=1 universe bounces at Planck density instead of hitting a big bang, yet still recollapses at the radius classical general relativity predicts.
Quantum Nature of the Big Bang: Improved dynamics
gr-qc 2006-07 conditional novelty 7.0 of 10

Tying the holonomy length to the Planck area gap instead of holding it constant makes the loop-quantum-cosmology bounce occur at the Planck density for any scalar-field momentum.
Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
gr-qc 2006-04 conditional novelty 7.0 of 10

In loop quantum cosmology, a flat homogeneous universe with a massless scalar field replaces the big-bang singularity with a deterministic quantum bounce connecting contraction and expansion.
Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
gr-qc 2005-04 accept novelty 7.0 of 10

Under semianalytic local diffeomorphism invariance, the holonomy-flux *-algebra admits exactly one Yang-Mills gauge invariant and diffeomorphism invariant state, the Ashtekar-Lewandowski state.
Black hole entropy from Quantum Geometry
gr-qc 2004-07 conditional novelty 7.0 of 10

A corrected count of black hole horizon states in loop quantum gravity shows that higher spins contribute, changing the derived Barbero-Immirzi parameter from its previously published value.
Covariant Hamiltonian Gravity in Spherical Symmetry
gr-qc 2026-11 accept novelty 6.0 of 10

The paper constructs an effective Einstein tensor from covariant Hamiltonian gravity and proves that generalized Vaidya solutions sourced by null dust exist for any static spherically symmetric vacuum family.
Axionic Wormholes in Metric-Affine Gravity
hep-ph 2026-09 conditional novelty 6.0 of 10

Metric-Affine Gravity with non-minimal couplings to curvature-like and topological terms can enhance the axionic wormhole action and alleviate the axion quality problem, with some parameter regions compatible with inflation.
Black holes with torsion hair in cubic Holst-type Poincar\'e gauge gravity: from singular to regular geometries
gr-qc 2026-09 reject novelty 6.0 of 10

In a cubic Holst-type Poincare gauge gravity model, the authors present exact spherically symmetric black hole families with torsion hair, including regular solutions with primary or secondary hair that violate the co...
Accretion dynamics of thin and thick disks in charged Kalb-Ramond black holes
gr-qc 2026-09 conditional novelty 6.0 of 10

For charged Kalb-Ramond black holes, the EHT shadow allows a broader range of the Lorentz-violation parameter l, and l systematically changes thin and thick disk emission and topology.
Coarse-grained models for loop quantum gravity and their renormalization
hep-th 2026-08 unverdicted novelty 6.0 of 10

The paper constructs coarse-grained Hilbert spaces and effective Hamiltonians for loop quantum gravity and writes down non-perturbative renormalization flow equations for them.
Absorption spectrum and greybody factors of charged black holes in loop quantum gravity
gr-qc 2026-08 conditional novelty 6.0 of 10

The absorption cross section of massless scalar waves by a charged loop-quantum-gravity black hole increases with the quantum parameter in an intermediate frequency band, decreases with charge, and matches classical a...
Integral Hilbert spaces and the dynamics of loop quantum cosmos
gr-qc 2026-08 conditional novelty 6.0 of 10

In a loop quantum cosmology model with negative cosmological constant, semiclassical states built by integrating over all superselection sectors behave no differently from single-sector states, with differences below ...
Exploring the near-kernel sector of quantum reduced loop gravity
gr-qc 2026-05 unverdicted novelty 6.0 of 10

Variational minimization of the squared Hamiltonian constraint in a truncated one-vertex loop gravity model yields three classes of near-kernel states; one factorized branch matches reduced Thiemann coherent states wi...
Lorentz Violation in Emergent Gravity and Its Cosmological Consequences
gr-qc 2025-11 conditional novelty 6.0 of 10

Emergent gravity is recast as an Otto cycle; adding work legs yields Lorentz violation and matter creation that can drive late-time cosmic acceleration.
Singularities in loop quantum cosmology
gr-qc 2025-07 unverdicted novelty 6.0 of 10

Loop quantum cosmology models harbor physical singularities or inconsistent space-time structures, with a new effective Friedmann equation revealing a sub-Planckian bounce after a singularity at infinite scale factor ...
Quasinormal modes of nonlocal gravity black holes
gr-qc 2025-07 conditional novelty 6.0 of 10

Quasinormal frequencies of nonlocal gravity black holes deviate from Schwarzschild values by up to about 12%, and the derived bounds on the model parameters α and k depend on projected detector sensitivity.
Dust shell in effective loop quantum black hole model
gr-qc 2025-06 conditional novelty 6.0 of 10

In a polymerized loop-quantum-gravity black hole model, a collapsing dust shell bounces and, for sufficiently heavy shells, follows a spacelike trajectory through the horizon, implying a finite horizon lifetime and a ...
Deep learning spinfoam vertex amplitudes: the Euclidean Barrett-Crane model
gr-qc 2025-05 conditional novelty 6.0 of 10

A proof-of-principle that simple neural networks can learn Euclidean Barrett-Crane 10j vertex amplitudes: classification generalizes to higher cutoffs, regression works only within the trained low-spin domain.
Radiative properties of a nonsingular black hole: Hawking radiation and gray-body factor
gr-qc 2025-04 conditional novelty 6.0 of 10

A singularity-free black hole radiates more coldly and more like a perfect black body than Schwarzschild does, and, on one assumption about its parameters, it ends as a zero-temperature remnant instead of evaporating.
The one-loop effective action from the coherent state path integral of loop quantum gravity
gr-qc 2025-02 conditional novelty 6.0 of 10

The one-loop effective action from the LQG coherent state path integral is computed and found to be UV-finite, with the dynamical area j0 > 0 at the quantum level.
Transition from Regular Black Holes to Wormholes in Covariant Effective Quantum Gravity: Scattering, Quasinormal Modes, and Hawking Radiation
gr-qc 2025-02 conditional novelty 6.0 of 10

For a quantum-corrected spacetime, the fundamental quasinormal mode differs little from Schwarzschild, higher overtones deviate significantly, and wormhole states have extremely long-lived modes.
Nonlocal gravity in a proper tetrad frame: traversable wormholes
gr-qc 2025-01 conditional novelty 6.0 of 10

Static, spherically symmetric traversable wormholes are built in revised Deser-Woodard nonlocal gravity by reconstructing the theory's distortion function from chosen wormhole metrics.
Conformal Cores of Quantum Black Holes in Quadratic Gravity
hep-th 2024-11 conditional novelty 6.0 of 10

Exact complex power-law solutions of pure quadratic gravity, named powerballs, can match a Schwarzschild black hole just outside its horizon and give a finite-action model of the quantum interior.
Perturbations of spinning black holes beyond General Relativity: Modified Teukolsky equation
gr-qc 2022-06 conditional novelty 6.0 of 10

A decoupled master equation for gravitational perturbations of non-Kerr, non-Ricci-flat spinning black holes is derived, extending Teukolsky's formalism to modified gravity at arbitrary spin.
Effective Spin Foam Models for Lorentzian Quantum Gravity
gr-qc 2021-04 conditional novelty 6.0 of 10

A Lorentzian version of the effective spin foam path integral is constructed and numerically probed, showing a semi-classical regime for small Barbero-Immirzi parameter on simple triangulations with one bulk triangle.
Edge modes of gravity -- II: Corner metric and Lorentz charges
hep-th 2020-07 conditional novelty 6.0 of 10

The corner metric of tetrad gravity satisfies an ultra-local sl(2,R) algebra whose Casimir is the corner area element, and its space-like nature places that Casimir in the unitary discrete series, giving a quantized a...
The Polymer representation for the scalar field: A Wigner functional approach
gr-qc 2019-08 conditional novelty 6.0 of 10

The polymer Wigner functional for a real scalar field is derived as a weak covariance limit of the Gaussian-measure Wigner functional, reproducing earlier GNS and Fock results.
Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
gr-qc 2016-02 conditional novelty 6.0 of 10

Effective Friedmann equations derived from group field theory condensates are non-singular: a conserved charge keeps the volume from reaching zero, producing a bounce in the Planck regime.
Loop quantization of the Schwarzschild interior revisited
gr-qc 2015-06 conditional novelty 6.0 of 10

Splitting the holonomy regularization into two direction-dependent parameters yields a loop quantization of the Schwarzschild interior that is independent of the fiducial cell and bounces into a white-hole spacetime w...
The Problem of Time and Quantum Cosmology in the Relational Particle Mechanics Arena
gr-qc 2011-11 conditional novelty 6.0 of 10

A relational three-particle toy model is used to argue for a local, conceptual resolution of the Problem of Time by combining emergent semiclassical time with histories and records.
Spinor Representation for Loop Quantum Gravity
gr-qc 2011-05 conditional novelty 6.0 of 10

Loop quantum gravity's edge Hilbert space is unitarily equivalent to a Bargmann space of holomorphic spinor functions, via an explicit map sending SU(2) representation matrices to holomorphic polynomials.
Twisted geometries: A geometric parametrisation of SU(2) phase space
gr-qc 2010-01 accept novelty 6.0 of 10

The loop gravity phase space on a fixed graph is symplectomorphic to a space of twisted geometries labeled by triangle areas, two unit normals, and an extrinsic angle per edge.
Cosmology of the Lifshitz universe
hep-th 2009-04 conditional novelty 6.0 of 10

A Lifshitz scalar coupled to Horava gravity produces bouncing vacuum cosmologies but, under detailed balance, an inflationary spectrum that is exponentially scale-dependent and observationally unviable.
Fractal Structure of Loop Quantum Gravity
gr-qc 2008-12 conditional novelty 6.0 of 10

Using the loop quantum gravity area spectrum, the author computes a spatial spectral dimension that runs from 2 at the Planck scale through 1.5 at intermediate scales to 3 at large scales.
Phase space descriptions for simplicial 4d geometries
gr-qc 2008-07 conditional novelty 6.0 of 10

On a fixed triangulation, the gauge-invariant phase space of loop quantum gravity is strictly larger than that of length or area Regge calculus and coincides with area-angle Regge calculus prior to the gluing constraints.
Anomaly freedom in perturbative loop quantum gravity
gr-qc 2008-06 conditional novelty 6.0 of 10

Non-trivial inverse-triad corrections can be implemented in anomaly-free effective constraints for cosmological perturbations, at the cost of adding counterterms whose coefficients are fixed by the requirement that th...
Stability analysis of sonic horizons in Bose-Einstein condensates
gr-qc 2006-03 conditional novelty 6.0 of 10

In 1D BECs, black-hole-like sonic horizons stay stable under both strict and relaxed boundary conditions, while white-hole and combined black-hole-white-hole configurations become unstable when downstream convergence ...
Quantum Gravity, Torsion, Parity Violation and all that
hep-th 2005-07 conditional novelty 6.0 of 10

Parity-violating gravitational interactions require a non-minimal fermion-torsion coupling, so real values of the Immirzi parameter remain unconstrained by parity experiments.
Quantum Gravity from Gluing Consistency: AdS/CFT to Spin-Foams
hep-th 2026-10 conditional novelty 5.0 of 10

This paper argues, with several internal consistency checks, that BF theory with conformal gauge group provides a universal gluing skeleton whose presentation-independence condition could bootstrap quantum gravity, li...
Dynamical dark energy from quantum gravity condensates
gr-qc 2026-09 conditional novelty 5.0 of 10

In a group field theory condensate model, order-six quantum gravity interactions drive an asymptotic de Sitter phase approached from the phantom side, with the effective cosmological constant depending on the interact...
A Minkowski-core black hole with cosmological constant and electric charge
gr-qc 2026-08 conditional novelty 5.0 of 10

A covariant effective Hamiltonian is built whose charged AdS/dS black hole has a Minkowski core, and its thermodynamics show an alpha-dependent phase transition.
Inflation in unimodular loop quantum cosmology
gr-qc 2026-07 conditional novelty 5.0 of 10

In unimodular loop quantum cosmology, an α-attractor potential allows a potential-energy-dominated bounce at the Planck scale that is consistent with CMB observations and may show quantum-gravity imprints.
Inflation from Covariant Signature Change: A Geometric Mechanism
gr-qc 2026-06 unverdicted novelty 5.0 of 10

A covariant signature-change layer between a Euclidean cap and a Lorentzian universe acts as a geometric, inflaton-free fluid that accelerates expansion while the interpolator slope exceeds a curvature-dependent threshold.
Higher-dimensional quantum-corrected Oppenheimer-Snyder model with a cosmological constant
gr-qc 2026-06 unverdicted novelty 5.0 of 10

Extends quantum Oppenheimer-Snyder collapse model to higher dimensions plus cosmological constant and reports modified AdS black-hole thermodynamics with finite small-black-hole temperature and an extra quantum-induce...
The problem of time: a path integral view
gr-qc 2026-05 unverdicted novelty 5.0 of 10

In a path-integral model of timeless quantum systems, time evolution arises when a clock is prepared in a semiclassical state, showing that the cosine problem in quantum gravity follows from time-reversal invariance a...
Unimodular quantum cosmology in the connection representation: A minimal model
gr-qc 2026-02 conditional novelty 5.0 of 10

In a flat, empty unimodular quantum cosmology in connection variables, positive-cosmological-constant wave functions vanish at zero volume, while a negative cosmological constant is excluded by operator regularity and...
Quantum Damping of Cosmological Shear: A New Prediction from Loop Quantum Cosmologies
gr-qc 2025-10 reject novelty 5.0 of 10

In mLQC-I, Bianchi I shear is claimed to decay exponentially after the bounce, producing isotropization independent of the matter content.
Effects of the ekpyrotic mechanism on inflationary phase in loop quantum cosmologies
gr-qc 2025-10 conditional novelty 5.0 of 10

In LQC and mLQC-I, tuned ekpyrotic-plus-inflation potentials can yield w>1 at the bounce and at least 60 e-folds of post-bounce inflation.
Motion of spinning particles around a quantum-corrected black hole without Cauchy horizons
gr-qc 2025-09 conditional novelty 5.0 of 10

For the covariant quantum-corrected black hole without Cauchy horizons, the effective potential, circular orbits, ISCO, and bound trajectories of spinning particles depend only weakly on the quantum parameter but stro...
Shadow constraints of charged black hole with scalar hair and gravitational waves from extreme mass ratio inspirals
gr-qc 2025-06 conditional novelty 5.0 of 10

EHT shadow data constrain the EMCS black hole charge and scalar hair to about 0.1 and 0.01 levels, while LISA EMRI waveforms could reach 0.01 and 0.0001 levels.
Periodic orbits and gravitational waveforms in quantum-corrected black hole spacetimes
gr-qc 2025-05 conditional novelty 5.0 of 10

For one effective quantum gravity black hole model (BH-I), the quantum parameter shifts periodic orbits and delays gravitational wave phase, while for the other model (BH-II) the effect is negligible, making BH-I pote...
Energy Extraction from Loop Quantum Black Holes: The Role of Magnetic Penrose Process and Quantum Gravity Effects with Astrophysical Insights
gr-qc 2024-12 conditional novelty 5.0 of 10

In the rotating loop quantum black hole spacetime, the maximum magnetic Penrose process efficiency decreases with the quantum parameter epsilon, from 20.7% at epsilon=0 to about 19.3% at the maximal spin for epsilon=0.3.

See all 101 Pith citations

How later papers used it

432 later papers cite it

Evidence: substantial. 421 of the citing papers share no author with it, and 26 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 655 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

5 later papers by other authors are listed below: 5 used its method or tool.

Uses its method or tool 5 of 17 papers with this label

Used the group averaging method from this paper, based on the Gel'fand triple, to correct the Gauss constraint solution.

Quantization of Lorentzian 3d Gravity by Partial Gauge Fixing (2012) · 1.00 · paraphrased: the licence does not allow quoting
Introduced a regularization analogous to the one used to define this paper's area operator of loop quantum gravity.

Loop Quantization of a Model for D=1+2 (Anti)de Sitter Gravity Coupled to Topological Matter (2014) · 1.00 · paraphrased: the licence does not allow quoting
Followed the lines of loop quantum gravity from this paper to construct a kinematical Hilbert space whose vectors are subjected to two constraints.

Loop quantization of a 3D Abelian BF model with sigma-model matter (2014) · 0.98 · paraphrased: the licence does not allow quoting
Followed this paper to remedy the problem that the decomposition into H_gamma was not orthogonal.

From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity (2012) · 0.94 · paraphrased: the licence does not allow quoting
Followed this paper and another work in its presentation of the construction of the group averaging map.

Dynamics in canonical models of loop quantum gravity (2019) · 0.80 · paraphrased: the licence does not allow quoting

How the literature uses it

403 arXiv papers cite this in 612 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 209 sentences without a confident label

Contests it 1 paper

Therefore, the omission of several (but not all) terms of order $ε^2$ in the original formulation of CLQG [ref] is not precise enough neither consistent.

Relativistic classical theory II. Holonomy-flux representation of gravitational degrees of freedom · Implementation of the holonomy representation · contest 0.90

Uses its method or tool 14 papers

In particular, the regularization procedure presented in this article is based mainly on Thiemann's regularization in canonical loop quantum gravity (CLQG) [ref] .

Relativistic classical theory II. Holonomy-flux representation of gravitational degrees of freedom · Equivalence principle on a lattice · 1.00
We will follow the standard group averaging method [ref] , based here on the Gel'fand triple [ref] $S_0$ $⊂$ $ℋ_Gauss$ $⊂S_0'$, where $S_0$ is the subspace of finite linear combinations of spin-networks defined at the end of the preceding subsection, dense in $ℋ_Gauss$, and $S_0'$ its dual, whose elements are the complex valued linear functionals $$ of $S_0$: : S_0 → , Ψ ↦ , Ψ∈ , linear-fnal where we use Schwartz notation $,$ for functionals [ref] .

The Hilbert space of Chern-Simons theory on the cylinder. A Loop Quantum Gravity approach · Diffeomorphism invariance · 0.99
Because we would like our construction to be background independent we will apply some ideas used in Loop Quantum Gravity (LQG) (see e.g. [ref] and references therein) to define the d.o.f.: since our configurational variable is a connection one-form $A$ a configuration elementary d.o.f. will be defined as a holonomy of the connection along a loop in $Σ$, similarly, since our momentum variable is a two-form a momentum elementary d.o.f. will be defined as an integral of it over a surface in $Σ$.

Constrained projective quantum states for the degenerate Plebanski gravity · Constrained projective quantum states for DPG · 0.85

Uses its data or values 1 paper

where $γ$ is the Barbero-Immirzi parameter[In the actual calculations further in the article we will use the value determined from black hole entropy counting [ref] equaling approximately $γ≈0.2375...$ as derived in [ref] .] and $Δ$ is the so-called area gap of LQC[The area gap is chosen to equal twice the lowest nonvanishing eigenvalue of the area operator in LQG.

Regularizations and quantum dynamics in loop quantum cosmology · Classical description and kinematics · 0.98

Compares with it 10 papers

The presented formulation is an order more precise than the formalism of CLQG [ref] , which has only a linear accuracy.

Relativistic classical theory II. Holonomy-flux representation of gravitational degrees of freedom · Regularization revisited · 0.93
The Hilbert space $F$ is the one proper to a system with infinitely many degrees of freedom[We point out a difference with respect to ordinary Loop Quantum Gravity [ref] where the infinitely many degrees of freedom are associated to a `quantum' configuration space consisting of distributional polymeric connections.

Loop Quantum Gravity a la Aharonov-Bohm · Perspectives · 0.96
Theorem [ref] basically states that the bulk of the spectrum found in loop quantum gravity [ref] , which is given by generalized connections with support on finite graphs, is excluded from the spectrum of $𝐇𝐃(M)$.

Quantum Holonomy Theory · The spectrum of $𝐇𝐃(M)$ · 0.93

Cites it as support 1 paper

The strongest reason for taking the kinematical picture described above seriously, in my opinion, is that it is the result of a rather conventional quantization of the phase space of general relativity [ref] .

A new look at loop quantum gravity · Derivation and relation with $SL(2,)$ · 0.99

Cites it as background 306 papers

This brings us to the second direction: canonical Loop Quantum Gravity [ref] .

Spin-foam model for gravity coupled to massless scalar field · Introduction · 0.81
Loop quantum cosmology (LQC) [ref] , which applies principles of loop quantum gravity (LQG) [ref] to cosmological settings, has been developed as a symmetry-reduced model of the full theory of LQG, to implement and test main ideas of LQG.

2+1 dimensional loop quantum cosmology of Bianchi I models · Introduction · 0.99
We will focus on a particular approach towards quantum gravity, namely Loop Quantum Gravity (LQG) [ref] .

Modifications to Gravitational Wave Equation from Canonical Quantum Gravity · Introduction · 0.99

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

Creutz M 1983 Quarks, gluons and lattices (Cambridge UP, Cambridge)

View on Pith 1983

[2] [2]

Ashtekar A 1991 Lectures on non-perturbative canonical gravity Notes prepared in collaboration with R. S. Tate (World Scientiﬁc, Singapore)

View on Pith 1991

[3] [3]

Baez J and Muniain J P 1994 Gauge ﬁelds, knots and gravity (World Scientiﬁc, Sin- gapore)

View on Pith 1994

[4] [4]

Gambini R and Pullin J 1996 Loops, knots, gauge theories and quantum gravity (Cam- bridge UP, Cambridge)

View on Pith 1996

[5] [5]

Carlip S 1998 Quantum gravity in 2+1 dimensions (Cambrige UP, Cambridge)

View on Pith 1998

[6] [6]

Rovelli C 1998 Loop quantum gravity Living Rev. Rel 1 1

View on Pith 1998

[7] [7]

Bojowald M. 2001 Quantum Geometry and Symmetry (Saker-Verlag, Aachen)

View on Pith 2001

[8] [8]

Ashtekar A 2002 Quantum geometry and gravity: Recent Adv ances General Relativ- ity and Gravitation ed Bishop N T and Maharaj S D (World Scientiﬁc, Singalore), gr-qc/0112038

View on Pith Pith review arXiv 2002

[9] [9]

Thiemann T 2002 Lectures on loop quantum gravity, to appe ar in Aspects of quantum gravity: From theory to experimental search Lecture Notes in Physics (Springer-Verlag, Berlin 2003), gr-qc/0210094 2004 Modern canonical quantum general relativity , (Cambridge University Press, Cam- bridge, in press), gr-qc/0110034

View on Pith Pith review arXiv 2002

[10] [10]

Perez A 2003 Spin foam models for quantum gravity Class. Quant. Grav. 20 R43–R104

View on Pith 2003

[11] [11]

C. Rovelli 2004 Quantum Gravity (Cambridge University Press, Cambridge, in press) Classical theory:

View on Pith 2004

[12] [12]

Ashtekar A 1986 New variables for classical and quantum gravity Phys. Rev. Lett. 57 2244–2247

View on Pith 1986

[13] [13]

Ashtekar A (1987) New Hamiltonian formulation of gener al relativity Phys. Rev. D36 1587–1602

View on Pith 1987

[14] [14]

Samuel J 1987 A Lagrangian basis for Ashtekar’s reformu lation of canonical gravity Pramana-J. Phys. 24 28 L429-L432 Jacobson T and Smolin L 1987 The left handed spin connection a s a variable for canonical greavity Phys. Lett. B196 39-42

View on Pith 1987

[15] [15]

Ashtekar A, Mazur P and Torre C G 1987 BRST structure of ge neral relativity in terms of new variables Phys. Rev D36 2955-2962

View on Pith 1987

[16] [16]

Ashtekar A, Romano J D and Tate R S 1989 New variables for g ravity: Inclusion of matter Phys. Rev. D40 2572–2587

View on Pith 1989

[17] [17]

Jacobson T 1988 New variables for canonical supergravi ty, Class. Quant. Grav. 5 923– 935 Matschull H J and Nicolai H 1994 Canonical Quantum Supergrav ity in three- dimensions Nucl. Phys. B411 609–646

View on Pith 1988

[18] [18]

Ashtekar A, Balachandran A P and Jo S 1989 The CP problem i n quantum gravity, Int. J. Mod. Phys. A4 1493—1514

View on Pith 1989

[19] [19]

Pleba´ nski J F 1977 On the separation of Einsteinian sub structures J. Math. Phys. 18 2511 115

View on Pith 1977

[20] [20]

Capovilla R, Dell J and Jacobson T 1989 General relativi ty without a metric Phys. Rev. Lett. 63 2325–2328 Capovilla R, Dell J, Jacobson T and Mason L 1991 Selfdual two f orms and gravity Class. Quant. Grav. 8 41–57

View on Pith 1989

[21] [21]

Holst S 1996 Barbero’s Hamiltonian derived from a gener alized Hilbert-Palatini action Phys. Rev. D53 5966-5969 Wisniewski J 2001 Symplectic structure from Holst action, p re-print

View on Pith 1996

[22] [22]

Samuel J 2000 Is Barbero’s Hamiltonian formulation a ga uge theory of Lorentzian gravity? Class. Quant. Grav. 17 L141-L148

View on Pith 2000

[23] [23]

Robinson D C 1995 A Lagrangian formalism for the Einstei n-Yang-Mills equations J. Math. Phys. 36 3733-42 Lewandowski J, Okol’ow A 2000 2-Form Gravity of the Lorentzi an Signature Class. Quant. Grav. 17 L47-L51

View on Pith 1995

[24] [24]

Alexandrov S, Livine E R 2003 SU(2) Loop Quantum Gravity seen from Covariant Theory Phys. Rev. D67 044009

View on Pith 2003

[25] [25]

Freidel L and Krasnov K 1999 BF description of higher dim ensional gravity theories Adv. Theor. Math. Phys. 3 1289–1324

View on Pith 1999

[26] [26]

Jacobson T, Romano J D 1992 Degenerate Extensions Of Gen eral Relativity Class. Quant. Grav. 9 L119–L124

View on Pith 1992

[27] [27]

Matschull H J 1996 Causal structure and diﬀeomorphisms in Ashtekar’s gravity Class. Quant. Grav. 13 765–782

View on Pith 1996

[28] [28]

Jacobson T 1996 (1+1) sector of (3+1) gravity Class. Quant. Grav. 13 L111–L116, Erratum-ibid. 1996 Class. Quant. Grav. 13 3269

View on Pith 1996

[29] [29]

Lewandowski J and Wisniewski J 1997 (2+1) sector of (3+1 ) gravity Class. Quant. Grav. 14 775–782

View on Pith 1997

[30] [30]

Lewandowski J and Wisniewski J 1999 Degenerate sectors of the Ashtekar gravity Class. Quant. Grav. 16 3057–3069

View on Pith 1999

[31] [31]

Penrose R 1976 Non-linear graviton and curved twistor t heory Gen. Rel.& Grav. 7 31-52

View on Pith 1976

[32] [32]

Ko M, Ludvigsen M, Newman E T and Tod P 1981 The theory of H space Phys. Rep. 71 51–139 Connections and loops:

View on Pith 1981

[33] [33]

Rovelli C and Smolin L 1988 Knot theory and quantum gravi ty Phys. Rev. Lett. 61 1155-1158

View on Pith 1988

[34] [34]

Rovelli C and Smolin L 1990 Loop representation for quan tum general relativity Nucl. Phys. B331 80–152

View on Pith 1990

[35] [35]

Ashtekar A, Husain V, Rovelli C, Samuel J, and Smolin L 19 89 2+1 quantum gravity as a toy model for the 3+1 theory Class. Quant. Grav. 6 L185–L193

View on Pith

[36] [36]

Ashtekar A, Rovelli C, and Smolin L 1991 Gravitons and lo ops Phys. Rev. D44 1740– 1755

View on Pith 1991

[37] [37]

Smolin L 1992 Recent developments in non-perturbative quantum gravity Quantum Gravity and Csomology ed Mercader J, Sol´ a J and Verdaguer R (World Scientiﬁc, Singapore)

View on Pith 1992

[38] [38]

Goldberg J N, Lewandowski J, Stornaiolo C 1992 Degenera cy in loop variables Com- 116 mun. Math. Phys. 148 377–402 Background independent quantization of theories of connec tions:

View on Pith 1992

[39] [39]

Ashtekar A and Isham C J 1992 Representation of the holon omy algebras of gravity and non-Abelian gauge theories Class. Quant. Grav. 9 1433–1467

View on Pith 1992

[40] [40]

Ashtekar A and Lewandowski J 1994 Representation theor y of analytic holonomy al- gebras, in Knots and Quantum Gravity ed Baez J C (Oxford U. Press, Oxford)

View on Pith 1994

[41] [41]

Baez J C 1994 Generalized measures in gauge theory Lett. Math. Phys. 31 213–223

View on Pith 1994

[42] [42]

Lewandowski J 1994 Topological Measure and Graph-Diﬀe rential Geometry on the Quotient Space of Connections Int. J. Mod. Phys. D3 207–210

View on Pith 1994

[43] [43]

Ashtekar A, Lewandowski L, Marolf D, Mour˜ ao J and Thiem ann T 1995 A manifestly gauge invariant approach to quantum gauge theories, in Geometry of Constrained Dy- namical Systems ed Charap J M (Cambridge U. Press, Cambridge)60–72

View on Pith 1995

[44] [44]

Marolf D and Mour˜ ao J 1995 On the support of the Ashtekar -Lewandowski measure Commun. Math. Phys. 170 583-606

View on Pith 1995

[45] [45]

Ashtekar A and Lewandowski J 1995 Projective technique s and functional integration Jour. Math. Phys. 36 2170–2191

View on Pith 1995

[46] [46]

Ashtekar A, Lewandowski L, Marolf D, Mour˜ ao J and Thiem ann T 1996 Coherent State Transforms for Spaces of Connections Jour. Funct. Analysis 135 519-551

View on Pith 1996

[47] [47]

Baez J C and Sawin S 1997 Functional integration on space s of connections Jour. Funct. Analysis 150 1–27

View on Pith 1997

[48] [48]

Ashtekar A, Corichi A and Zapata J A 1998 Quantum theory o f geometry: III. Non- commutativity of Riemannian structures Class. Quant. Grav. 15 2955–2972

View on Pith 1998

[49] [49]

Marolf D, Mour˜ ao J, Thiemann T 1997 The Status of Diﬀeom orphism Superselection in Euclidean 2+1 Gravity J. Math. Phys. 38 4730-4740

View on Pith 1997

[50] [50]

Mour˜ ao J M, Thiemann T, Velhinho J M 1999 Physical Prope rties of Quantum Field Theory Measures J. Math. Phys. 40 2337–2353

View on Pith 1999

[51] [51]

Velhinho J M 2002 A groupoid approach to spaces of genera lized connections J. Geom. Phys. 41 166–180

View on Pith 2002

[52] [52]

Fleischhack C 2000 Stratiﬁcation of the Generalized Ga uge Orbit Space Commun. Math. Phys. 214 607–649

View on Pith 2000

[53] [53]

Fleischhack C 2003 On the Gribov Problem for Generalize d Connections Commun. Math. Phys. 234 423–454

View on Pith 2003

[54] [54]

Fleischhack C 2003 Hyphs and the Ashtekar-Lewandowski Measure J. Geom. Phys. 45 231–251

View on Pith 2003

[55] [55]

Sahlmann H 2002 When Do Measures on the Space of Connecti ons Support the Triad Operators of Loop Quantum Gravity? Preprint gr-qc/0207112 Sahlmann H 2002 Some Comments on the Representation Theory o f the Algebra Un- derlying Loop Quantum Gravity Preprint gr-qc/0207111

View on Pith Pith review arXiv 2002

[56] [56]

Oko l´ ow A, Lewandowski J 2003 Diﬀeomorphism covariant represen tations of the holonomy-ﬂux star-algebra Class. Quant. Grav. 20 3543–3568

View on Pith 2003

[57] [57]

Sahlmann H and Thiemann T 2003 On the superselection the ory of the Weyl algebra for diﬀeomorphism invariant quantum gauge theories Preprint gr-qc/0302090 Sahlmann H and Thiemann T 2003 Irreducibility of the Ashteka r-Isham-Lewandowski representation Preprint gr-qc/0303074 117

View on Pith Pith review arXiv 2003

[58] [58]

Lewandowski J, Oko l´ ow A, Sahlmann H, Thiemann T 2003 Uniqueness of the diﬀeo- morphism invariant state on the quantum holonomy-ﬂux algeb ra Preprint Spin networks:

View on Pith 2003

[59] [59]

Penrose R 1971 Angular momentum: an approach to combina torial space-time Quan- tum Theory and Beyond ed Bastin T (Cambridge University Press)

View on Pith 1971

[60] [60]

Rovelli C and Smolin L 1995 Spin networks and quantum gra vity Phys. Rev. D52 5743–5759

View on Pith 1995

[61] [61]

Baez J C 1996 Spin networks in non-perturbative quantum gravity, in The Interface of Knots and Physics ed Kauﬀman L (American Mathematical Society, Providence) pp. 167–203 Baez J C 1996 Spin networks in gauge theory Adv. Math.117 253–272

View on Pith 1996

[62] [62]

Thiemann T 1998 The inverse loop transform J. Math. Phys. 39 1236–1248

View on Pith 1998

[63] [63]

Baez J C and Sawin S 1998 Diﬀeomorphism–invariant spin n etwork states Jour. Funct. Analysis 158 253–266

View on Pith 1998

[64] [64]

C Fleischhack 2003 Proof of a Conjecture by Lewandowski and Thiemann Preprint math-ph/0304002 Geometric operators and their properties

View on Pith Pith review arXiv 2003

[65] [65]

Rovelli C and Smolin L 1995 Discreteness of area and volu me in quantum gravity Nucl. Phys. B442 593–622; Erratum: Nucl. Phys. B456 753

View on Pith 1995

[66] [66]

Ashtekar A and Lewandowski L 1995 Diﬀerential geometry on the space of connections using projective techniques Jour. Geo. & Phys. 17 191–230

View on Pith 1995

[67] [67]

Loll R 1995 The volume operator in discretized quantum g ravity Phys. Rev. Lett. 75 3048–3051

View on Pith 1995

[68] [68]

Loll R 1995 Spectrum of the Volume Operator in Quantum Gr avity Nucl. Phys. B460 143–154

View on Pith 1995

[69] [69]

Frittelli S, Lehner L and Rovelli C 1996 Class. Quant. Grav. 13 2921–2932

View on Pith 1996

[70] [70]

De Pietri R, Rovelli C 1996 Phys. Rev. D54 2664–2690

View on Pith 1996

[71] [71]

Lewandowski J. 1997 Volume and Quantizations Class. Quant. Grav. 14 71–76

View on Pith 1997

[72] [72]

Ashtekar A and Lewandowski J 1997 Quantum theory of geom etry I: Area operators Class. Quant. Grav. 14 A55–A81

View on Pith 1997

[73] [73]

Ashtekar A and Lewandowski J 1997 Quantum theory of geom etry II: Volume Opera- tors Adv. Theo. Math. Phys. 1 388–429

View on Pith 1997

[74] [74]

Loll R 1997 Simplifying the spectral analysis of the vol ume operator Nucl. Phys. B500 405–420

View on Pith 1997

[75] [75]

Loll R 1997 Further results on geometric operators in qu antum gravity Class. Quant. Grav. 14 1725–1741

View on Pith 1997

[76] [76]

De Pietri R 1997 Spin Networks and Recoupling in Loop Qua ntum Gravity Nucl. Phys. Suppl 57 251-254

View on Pith 1997

[77] [77]

De Pietri R 1997 On the relation between the connection a nd the loop representation of quantum gravity Class. Quant. Grav. 14 53–70

View on Pith 1997

[78] [78]

Thiemann T 1998 Closed formula for the matrix elements o f the volume operator in canonical quantum gravity J. Math. Phys. 39 3347-3371

View on Pith 1998

[79] [79]

Thiemann T 1998 A length operator for canonical quantum gravity Jour. Math. Phys. 118 39 3372–3392

View on Pith 1998

[80] [80]

Major S A 1999 Operators for quantized directions Class. Quant. Grav. 16 3859-3877 Barbero-Immirzi ambiguity

View on Pith 1999

[81] [81]

Barbero F 1996 Real Ashtekar variables for Lorentzian s ignature space-times Phys. Rev. D51 5507–5510

View on Pith 1996

[82] [82]

Immirzi G 1997 Quantum gravity and Regge calculus Nucl. Phys. Proc. Suppl. 57 65–72

View on Pith 1997

[83] [83]

Rovelli C. and Thiemann T. (1998) The Immirizi paramete r in quantum general rela- tivity Phys. Rev. D57 1009–1014

View on Pith 1998

[84] [84]

Gambini R, Obregon O and Pullin J 1999 Yang-Mills analog s of the Immirzi ambiguity Phys. Rev. D59 047505 Quantum Einstein’s equation I

View on Pith 1999

[85] [85]

Kuchaˇ r K 1993 Canonical Quantum Gravity General Relativity and Gravitation 1992 ed Gleiser R J, Kozameh C N, Moreschi O M (Institute of Physics Publishing) 119–150

View on Pith 1993

[86] [86]

Ashtekar A, Tate R S and Uggla C 1993 Minisuperspaces: Ob servables and quantiza- tion Int. J. Phys. D2 15–50 Ashtekar A, Tate R S and Uggla C 1993 Minisuperspaces: Symmet ries and quantiza- tion Misner Festschrift ed Hu B L et al (Cambridge U. P., Cambridge)

View on Pith 1993

[87] [87]

Ashtekar A and Tate R S 1994 An algebraic extension of Dir ac quantization: Examples Jour. Math. Phys. 35 6434–6470

View on Pith 1994

[88] [88]

Marolf D 1995 Reﬁned algebraic quantization: Systems w ith a single constraint Preprint gr-qc/9508015

View on Pith Pith review arXiv 1995

[89] [89]

Ashtekar A, Lewandowski J, Marolf D, Mour˜ ao J and Thiem ann T 1995 Quantization of diﬀeomorphism invariant theories of connections with lo cal degrees of freedom Jour. Math. Phys. 36 6456–6493

View on Pith 1995

[90] [90]

Marolf D, Mour˜ ao J and Thiemann T 1997 The status of diﬀe omorphism super- selection in Euclidean 2+1 gravity J. Math. Phys. 38 4730-4740

View on Pith 1997

[91] [91]

Guilini N and Marolf D 1999 On the Generality of Reﬁned Al gebraic Quantization Class. Quant. Grav. 16 2479–2488 A uniqueness theorem for constraint quantization Class. Quant. Grav. 16 2489–2505

View on Pith 1999

[92] [92]

Lewandowski J and Thiemann T 1999 Diﬀeomorphism invari ant quantum ﬁeld theories of connections in terms of webs Class. Quant. Grav. 16 2299–2322

View on Pith 1999

[93] [93]

Corichi A and Zapata J A 1997 On diﬀeomorphism invarianc e for lattice theories Nucl. Phys. B493 475–490 Quantum Einstein’s equation II

View on Pith 1997

[94] [94]

Rovelli C and Smolin L 1994 The physical Hamiltonian in n onperturbative quantum gravity Phys. Rev. Lett. 72 446–449

View on Pith 1994

[95] [95]

Thiemann T 1996 Anomaly-free formulation of non-pertu rbative, four-dimensional Lorentzian quantum gravity Phys. Lett. B380 257–264

View on Pith 1996

[96] [96]

Thiemann T 1998 Quantum spin dynamics (QSD) Class. Quant. Grav. 15 839–873

View on Pith 1998

[97] [97]

Thiemann T. 1998 QSD III: Quantum constraint algebra an d physical scalar product in quantum general relativity Class. Quant. Grav. 15 1207–1247 119

View on Pith 1998

[98] [98]

Thiemann T 1998 QSD V: Quantum gravity as the natural reg ulator of matter quantum ﬁeld theories Class. Quant. Grav. 15 1281–1314

View on Pith 1998

[99] [99]

Thiemann T 2001 Quantum Spin Dynamics (QSD) : VII. Sympl ectic Structures and Continuum Lattice Formulations of Gauge Field Theories Class. Quant. Grav. 18 3293– 3338

View on Pith 2001

[100] [100]

Gambini R, Lewandowski J, Marolf D and Pullin J 1998 On t he consistency of the constraint algebra in spin network quantum gravity Int. J. Mod. Phys. D7 97–109

View on Pith 1998

[101] [101]

Lewandowski J and Marolf D 1998 Loop constraints: A hab itat and their algebra Int. J. Mod. Phys. D7 299–330

View on Pith 1998

[102] [102]

Gaul G and Rovelli C 2001 Generalized hamiltonian cons traint operator in loop quan- tum gravity and its simplest Euclidean matrix elements Class. Quant. Grav. 18 1593– 1624 Big-bang:

View on Pith 2001

[103] [103]

Kodama H 1988 Specialization of Ashtekar’s formalism to Bianchi cosmology Prog. Theor. Phys. 80 1024–1040 Kodama H 1990 Holomorphic wavefunction of the universe Phys. Rev. D42 2548–2565

View on Pith 1988

[104] [104]

Bojowald M 2001 Absence of singularity in loop quantum cosmology Phys. Rev. Lett. 86 5227–5230

View on Pith 2001

[105] [105]

Bojowald M 2001 Inverse scale factor in isotropic quan tum geometry Phys. Rev. D64 084018

View on Pith 2001

[106] [106]

Bojowald M 2001 Dynamical initial conditions in quant um cosmology Phys. Rev. Lett. 87 121301

View on Pith 2001

[107] [107]

Bojowald M 2001 Loop Quantum Cosmology IV: Discrete Ti me Evolution Class. Quant. Grav. 18 1071–1088

View on Pith 2001

[108] [108]

Bojowald M 2001 Loop quantum cosmology III: Wheeler-D eWitt operators Class. Quant. Grav. 18 1055–1070 Bojowald M 2002 The Semiclassical Limit of Loop Quantum Cosm ology Class. Quant. Grav. 18 L109–L116

View on Pith 2001

[109] [109]

Bojowald M 2001 The Inverse Scale Factor in Isotropic Q uantum Geometry Phys.Rev. D64 084018

View on Pith 2001

[110] [110]

Bojowald M 2002 Isotropic Loop Quantum Cosmology Class.Quant.Grav. 19 2717– 2742

View on Pith 2002

[111] [111]

Bojowald M, Hinterleitner F 2002 Isotropic Loop Quant um Cosmology with Matter Phys.Rev. D66 104003

View on Pith 2002

[112] [112]

Bojowald M and Vandersloot K 2003 Loop Quantum Cosmolo gy, Boundary Proposals, and Inﬂation Phys.Rev. D67 124023

View on Pith 2003

[113] [113]

Bojowald M 2003 Homogeneous Loop Quantum Cosmology Class.Quant.Grav. 20 2595–2615

View on Pith 2003

[114] [114]

Bojowald M 2003 Initial Conditions for a Universe Gen. Rel. Grav. 35, 1877-1883 (First Prize in the Gravity Research Foundation Essay Conte st)

View on Pith 2003

[115] [115]

Ashtekar A, Bojowald M, Lewandowski J 2003 Mathematic al structure of loop quantum cosmology Adv. Theor. Math. Phys. 7 233–268

View on Pith 2003

[116] [116]

Bojowald M, Date G and Vandersloot K 2004 Homogeneous L oop Quantum Cosmol- ogy: The Role of the Spin Connection Class. Quant. Grav. textbf21 1253-1278 120

View on Pith 2004

[117] [117]

Ashtekar A, Bojowald M and Willis J 2004 Quantum correc tions to Friedmann equa- tions in loop quantum cosmology (in preparation) Black holes:

View on Pith 2004

[118] [118]

Bekenstein J D 1973 Black holes and entropy Phys. Rev. D7 2333–2346 (1974) Generalized second law of thermodynamics in black ho le physics Phys. Rev. D9 3292–3300 Bekenstein J D and Meisels A 1977 Einstein A and B coeﬃcients f or a black hole Phys. Rev. D15 2775–2781

View on Pith 1974

[119] [119]

Bardeen J W, Carter B and Hawking S W 1973 The four laws of black hole mechanics Commun. Math. Phys. 31 161-170

View on Pith 1973

[120] [120]

Hawking S W 1975 Particle creation by black holes Commun. Math. Phys. 43 199–220

View on Pith 1975

[121] [121]

Gibbons G and Hawking S W 1977 Cosmological event horiz ons, thermodynamics, and particle creation Phys. Rev. D15 2738–2751

View on Pith 1977

[122] [122]

Smolin L 1995 Linking topological quantum ﬁeld theory and nonperturbative quantum gravity J. Math. Phys. 36 6417–6455

View on Pith 1995

[123] [123]

Barreira M, Carfora M and Rovelli C 1996 Physics with no n-perturbative quantum gravity: radiation from a quantum black hole Gen. Rel. Grav. 28 1293–1299 Rovelli C 1996 Black hole entropy from loop quantum gravity Phys. Rev. Lett. 14 3288–3291 Rovelli C 1996 Loop quantum gravity and black hole physics Helv. Phys. Acta. 69 582–611

View on Pith 1996

[124] [124]

Krasnov K 1997 Geometrical entropy from loop quantum g ravity Phys. Rev. D55 3505–3513 Krasnov K 1998 On statistical mechanics of Schwarzschild bl ack holes Gen. Rel. Grav. 30 53–68

View on Pith 1997

[125] [125]

Jacobson T, Kang G and Myers R C 1994 On black hole entrop y Phys. Rev. D49 6587–6598

View on Pith 1994

[126] [126]

Wald R. (1993) Black hole entropy is Noether charge Phys. Rev. D48 3427–3431 Iyer V and Wald R 1994 Some properties of Noether charge and a p roposal for dynam- ical black hole entropy Phys. Rev. D50 846–864

View on Pith 1993

[127] [127]

Ashtekar A, Baez J C, Corichi A, and Krasnov K 1998 Quant um geometry and black hole entropy (1998) Phys. Rev. Lett. 80 904–907

View on Pith 1998

[128] [128]

Ashtekar A, Corichi A and Krasnov K 1999 Isolated horiz ons: the classical phase space Adv. Theor. Math. Phys. 3 418–471

View on Pith 1999

[129] [129]

Ashtekar A, Baez J C and Krasnov K 2000 Quantum geometry of isolated horizons and black hole entropy Adv. Theo. Math. Phys. 4 1–95

View on Pith 2000

[130] [130]

Kaul R K and Majumdar P 2000 Logarithmic corrections to the Bekenstein-Hawking entropy Phys. Rev. Lett. 84 5255–5257

View on Pith 2000

[131] [131]

Ashtekar A, Beetle C and Fairhurst S 1999 Isolated hori zons: a generalization of black hole mechanics Class. Quantum Grav. 16 L1–L7 Ashtekar A, Beetle C and Fairhurst S 2000 Mechanics of isolat ed horizons Class. Quan- tum Grav. 17 253–298

View on Pith 1999

[132] [132]

Lewandowski J 2000 Space-times admitting isolated ho rizons Class. Quantum Grav. 17 L53–L59 121

View on Pith 2000

[133] [133]

Ashtekar A, Fairhurst S and Krishnan B 2000 Isolated Ho rizons: Hamiltonian Evolu- tion and the First Law Phys. Rev. D62 104025

View on Pith 2000

[134] [134]

Ashtekar A, Beetle C and Lewandowski J 2001 Mechanics o f rotating isolated horizons Phy. Rev. D64 044016

View on Pith 2001

[135] [135]

Ashtekar A, Beetle C and Lewandowski J 2002 Geometry of generic isolated horizons Class. Quantum Grav. 19 1195–1225

View on Pith 2002

[136] [136]

Ashtekar A, Corichi A and Sudarski D 2003 Non-Minimall y Coupled Scalar Fields and Isolated Horizons Class. Quantum Grav. 20 3413-3425

View on Pith 2003

[137] [137]

Ashtekar A and Corichi A 2003 Non-minimal couplings, q uantum geometry and black hole entropy 20 Class. Quantum Grav. 20 4473-4484

View on Pith 2003

[138] [138]

Ashtekar A, Engle J, Pawlowski, T and van der Broeck C 20 04 Multipole moments of isolated horizons Class. Quant. Grav. 21 2549-2570

View on Pith

[139] [139]

Ashtekar A 2003 Black hole entropy: Inclusion of disto rtion and angular momentum, http://www.phys.psu.edu/events/index.html?event id=517&event type=17 Ashtekar A, Engle J and van der Broeck C 2004 (in preparation)

View on Pith 2003

[140] [140]

Wheeler J A 1992 It from bit Sakharov Memorial Lectures on Physics, Vol 2 ed Keldysh L and Feinberg V (Nova Science, Moscow)

View on Pith 1992

[141] [141]

Ghosh A and Mitra P 2004 A bound on the log correction to t he black hole area law pre-print gr-qc/0401070 Low energy physics:

View on Pith Pith review arXiv 2004

[142] [142]

Ashtekar A, Rovelli C and Smolin L 1992 Weaving a classi cal geometry with quantum threads Phy. Rev. Lett. 69 237–240

View on Pith 1992

[143] [143]

Arnsdorf M, Gupta S 2000 Loop quantum gravity on non-co mpact spaces Nucl. Phys. B577 529-546

View on Pith 2000

[144] [144]

Corichi A, Reyes J M 2001 A Gaussian Weave for Kinematic al Loop Quantum Gravity Int. J. Mod. Phys. D10 325-338

View on Pith 2001

[145] [145]

Hall B C 1994 The Segal-Bergmann coherent state transf orm for compact Lie Lie groups J. Funct. Anal. 122 103-151

View on Pith 1994

[146] [146]

Sahlmann H, Thiemann T and Winkler O 2001 Coherent stat es for canonical quantum general relativity and the inﬁnite tensor product extensio n Nucl. Phys. B606 401-440

View on Pith 2001

[147] [147]

Thiemann T 2001 Gauge ﬁeld theory coherent states (GCS ): I. general properties Class. Quant. Grav. 18 2025-2064 T. Thiemann, O. Winkler 2001 Gauge Field Theory Coherent Sta tes (GCS) : II. Peakedness Properties Class. Quant. Grav. 18 2561–2636 Thiemann T, Winkler O 2001 Gauge Field Theory Coherent State s (GCS) : III. Ehren- fest Theorems Class. Quant. G...

View on Pith 2001

[148] [148]

Hanno Sahlmann, Thomas Thiemann 2002 Towards the QFT o n Curved Spacetime Limit of QGR. I: A General Scheme Preprint gr-qc/0207030 Sahlmann H Thomas Thiemann 2002 Towards the QFT on Curved Spa cetime Limit of QGR. II: A Concrete Implementation Preprint gr-qc/0207031

View on Pith Pith review arXiv 2002

[149] [149]

Thiemann T 2002 Complexiﬁer Coherent States for Quant um General Relativity Preprint gr-qc/0206037 122

View on Pith Pith review arXiv 2002

[150] [150]

Bombelli L 2002 Statistical geometry of random weave s tates Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity ed Gurzadyan VG, Jantzen RT, and Ruﬃni R (World Scientiﬁc, Singapore) gr-qc/0101080

View on Pith Pith review arXiv 2002

[151] [151]

Ashtekar A and Isham C J 1992 Phys. Lett. B274 393-398

View on Pith 1992

[152] [152]

Varadarajan M 2000 Fock representations from U(1) hol onomy algebras Phys. Rev. D61 104001 Varadarajan M. (2001) M. Photons from quantized electric ﬂu x representations Phys. Rev. D64 104003

View on Pith 2001

[153] [153]

Ashtekar A and Lewandowski J 2001 Relation between pol ymer and Fock excitations Class. Quant. Grav. 18 L117–L127

View on Pith 2001

[154] [154]

Velhinho J M 2002 Invariance properties of induced Foc k measures for U(1) holonomies Commun. Math. Phys. 227 541–550

View on Pith 2002

[155] [155]

Ashtekar A, Fairhurst S and Willis J 2003 Quantum gravi ty, shadow states, and quan- tum mechanics Class. Quantum Grav. 20, 1031-1061

View on Pith 2003

[156] [156]

Ashtekar A, Fairhurst S and Ghosh A 2004 (in preparatio n)

View on Pith 2004

[157] [157]

Varadarajan M. 2002 Gravitons from a loop representat ion of linearised gravity Phys. Rev. D66 024017

View on Pith 2002

[158] [158]

Ashtekar A, Ghosh A and Van Den Broeck C 2004 (in prepara tion)

View on Pith 2004

[159] [159]

Bobienski M, Lewandowski J, Mroczek M 2002 A 2-Surface Quantization of the Lorentzian Gravity Proceedings of the Ninth Marcel Grossmann Meeting on Genera l Relativity ed Gurzadyan VG, Jantzen RT, and Ruﬃni R (World Scientiﬁc, Si ngapore) gr-qc/0101069

View on Pith Pith review arXiv 2002

[160] [160]

Ashtekar A, Lewandowski J and Sahlmann H 2003 Polymer a nd Fock representations of a scalar ﬁeld Class. Quant. Grav. 20 L11–L21 Spin foams and ﬁniteness:

View on Pith 2003

[161] [161]

Baez J C 2000 An introduction to spin foam models of quan tum gravity and BF theory Lect. Notes Phys. 543 25–94

View on Pith 2000

[162] [162]

Baez J C 1998 Spin foam models Class. Quant. Grav. 15 1827–1858

View on Pith 1998

[163] [163]

Reisenberger M P 1997 A lattice worldsheet sum for Reis enberger M P 1997 4-d Eu- clidean general relativity Preprint gr-qc/9711052 Reisenberger M P 1999 On relativistic spin network vertices J. Math. Phys. 40 2046– 2054

View on Pith Pith review arXiv 1997

[164] [164]

Reisenberger M P and Rovelli C 2001 Spacetime as a Feynm an diagram: the connection formulation Class. Quant. Grav. 18 121–140 Reisenberger M P and Rovelli 2002 Spacetime states and covar iant quantum theory Phys. Rev. D65 125016

View on Pith 2001

[165] [165]

Barrett J W and Crane L 1998 Relativistic spin networks and quantum gravity J. Math. Phys. 39 3296–3302 Barrett J W and Crane L 2000 A Lorentzian signature model for q uantum general relativity Class. Quant. Grav. 17 3101–3118

View on Pith 1998

[166] [166]

Perez A 2001 Finiteness of a spinfoam model for Euclide an quantum general relativity Nucl. Phys. B599 427–434 Perez A and Rovelli C 2001 Spin foam model for Lorentzian gene ral relativity Phys. Rev. D63 041501 123 Crane L, Perez A and Rovelli C 2001 Perturbative ﬁniteness in spin-foam quantum gravity Phys. Rev. Lett. 87 181301 Crane L, Perez A and Rovell...

View on Pith 2001

[167] [167]

Baez J, Christensen D, Halford T R, Tsang DC 2002 Spin Fo am Models of Riemannian Quantum Gravity Class. Quant. Grav. 194627-4648

View on Pith 2002

[168] [168]

Gambini R and Pullin J 2002 A ﬁnite spin-foam-based the ory of three and four dimen- sional quantum gravity Phys. Rev. D66 024020

View on Pith 2002

[169] [169]

Lauscher O and Reuter M 2002 Is quantum Einstein gravit y non-perturbatively renor- malizable? Class. Quant. Grav. 19 483–492

View on Pith 2002

[170] [170]

Percacci R and Perini D 2003 Asymptotic safety of gravi ty coupled to matter Phys. Rev. D68044018 Perini D 2003 Gravity and matter with asymptotic safety pre-print hep-th/0305053

View on Pith Pith review arXiv 2003

[171] [171]

Bojowald M and Perez A 2003 Spin foam quantization and a nomalies gr-qc/0303026

View on Pith Pith review arXiv 2003

[172] [172]

Freidel L and Louapre D 2003 Diﬀeomorphisms and spin fo am models, Nucl.Phys. B662 279-298 Freidel L and Louapre D 2003 Non-perturbative summation ove r 3D discrete topologies Phys. Rev. D68 104004 hep-th/0211026

View on Pith Pith review arXiv 2003

[173] [173]

Perez A and Noui K 2004 Three dimensional loop quantum g ravity: coupling to point particles pre-print gr-qc/0402111 2004 Three dimensional loop quantum gravity: physical scal ar product and spin foam models pre-print gr-qc/0402110 Outlook:

View on Pith Pith review arXiv 2004

[174] [174]

Ashtekar A, Lewandowski J, Marolf D, Mour˜ ao J and Thiemann T 1997 SU(N) Quan- tum Yang-Mills theory in two dimensions: A complete solutio n J. Math. Phys. 38, 5453-5482

View on Pith 1997

[175] [175]

Ashtekar A and Sahlmann H 2004 (in preparation)

View on Pith 2004

[176] [176]

Okolw A 204 Representations of quantum geometry Ph.D. thesis, University of Warsaw

View on Pith

[177] [177]

Rovelli C and Speziale S 2003 Reconcile Planck-scale d iscreteness and the Lorentz- Fitzgerald contraction Phys. Rev. D67 064019

View on Pith 2003

[178] [178]

Thiemann T 2003 The Phoenix project: Master constrain t programme for loop quan- tum gravity Preprint gr-qc/0305080

View on Pith Pith review arXiv 2003

[179] [179]

Dittrich B 2004 Testing the master constraint program me for loop quantum gravity http://www.phys.psu.edu/events/index.html?event id=850&event type=17

View on Pith 2004

[180] [180]

Klauder J 2003 Aﬃne quantum gravity Int. J. Mod. Phys. D12 1769-1774 2004 The utility of coherent states and other mathematical m ethods in the foundations of aﬃne quantum gravity, pre-print hep-th/0401214

View on Pith Pith review arXiv 2003

[181] [181]

Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Consi stent canonical quantiza- tion of general relativity in the space of Vassiliev knot inv ariants Phys. Rev. Lett. 84 2314–2317 2000 Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical struc- ture Class. Quant. Grav. 17 3211-3238 2000 Canonical quantum gravity in the Vassiliev...

View on Pith 2000

[182] [182]

Gambini R and Pullin J 2003 Canonical quantization of g eneral relativity in discrete space-times Phys. Rev. Lett. 90 021301 Gambini R, Porto R and Pullin J 2004 Loss of coherence from dis crete quantum gravity Class. Quant. Grav. 21 L51-L57 Gambini R, Porto R and Pullin J 2004 A relational solution to t he problem of time in quantum mechanics and quantum...

View on Pith Pith review arXiv 2003

[183] [183]

Horowitz G. T. 1998 Quantum states of black holes, in Black Holes and Relativistic Stars, ed Wald R M ( University of Chicago Press, Chicago)

View on Pith 1998

[184] [184]

Carlip S 1999 Entropy from Conformal Field Theory at Ki lling Horizons Class. Quant. Grav. 16 3327–3348

View on Pith 1999

[185] [185]

Dreyer O, Ghosh A and Wisniewski J 2001 Black hole entro py calculations based on symmetries, Class. Quant. Grav. 18 1929-1938

View on Pith 2001

[186] [186]

Carlip S 2002 Near-Horizon Conformal Symmetry and Bla ck Hole Entropy Phys. Rev. Lett. 88 241301

View on Pith 2002

[187] [187]

Ashtekar A, Krishnan B 2002 Dynamical Horizons: Energ y, Angular Momentum, Fluxes and Balance Laws, Phys. Rev. Lett. 89 261101 2003 Dynamical horizons and their properties, Phys. Rev. D68 104030

View on Pith 2002

[188] [188]

Bojowald M 2002 Inﬂation from Quantum Geometry Phys.Rev.Lett. 89 261301

View on Pith 2002

[189] [189]

Bojowald M and Date G 2004 Quantum suppression of the ge neric chaotic behavior close to cosmological singularities Phys. Rev. Lett. 92 071302

View on Pith 2004

[190] [190]

Tsujikawa S, Singh P and Maartens R 2003 Loop quantum gr avity eﬀects on inﬂation and the CMB, pre-print astro-ph/0311015 125

View on Pith Pith review arXiv 2003