RECORD
Holonomy-flux spinfoam amplitude
General Relativity and Quantum Cosmology · Submitted 20 Nov 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For small heat kernel `time' the spinfoam amplitude is peaked on classical space-time geometries, where at most countably many curvatures are allowed for non-zero Barbero-Immirzi parameter.
The compiled record
The paper's own sentences, arranged. 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.
Open the compiled record
The abstract, sentence by sentence
We introduce a holomorphic representation for the Lorentzian EPRL spinfoam on arbitrary 2-complexes. The representation is obtained via the Ashtekar-Lewandowski-Marolf-Mour\~ao-Thiemann heat kernel coherent state transform. The new variables are classical holonomy-flux phase space variables $(h,X)\simeq \mathcal T^*SU(2)$ of Hamiltonian loop quantum gravity prescribing the holonomies of the Ashtekar connection $A=\Gamma + \gamma K$, and their conjugate gravitational fluxes. For small heat kernel `time' the spinfoam amplitude is peaked on classical space-time geometries, where at most countably many curvatures are allowed for non-zero Barbero-Immirzi parameter. We briefly comment on the possibility to use the alternative flipped classical limit.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We introduce a holomorphic representation for the Lorentzian EPRL spinfoam on arbitrary 2-complexes. | contribution 1.00 | 0.94 | 0.21 | asserted 1.00 |
| s1 | The representation is obtained via the Ashtekar-Lewandowski-Marolf-Mour\~ao-Thiemann heat kernel coherent state transform. | method 0.96 | 0.62 | 0.05 | asserted 1.00 |
| s2 | The new variables are classical holonomy-flux phase space variables $(h,X)\simeq \mathcal T^*SU(2)$ of Hamiltonian loop quantum gravity prescribing the holonomies of the Ashtekar connection $A=\Gamma + \gamma K$, and their conjugate gravitational fluxes. | method 0.65 | 0.24 | 0.07 | asserted 1.00 |
| s3 | For small heat kernel `time' the spinfoam amplitude is peaked on classical space-time geometries, where at most countably many curvatures are allowed for non-zero Barbero-Immirzi parameter. | result 0.97 | 0.82 | 0.48 | asserted 0.98 |
| s4 | We briefly comment on the possibility to use the alternative flipped classical limit. | future work 0.97 | 0.36 | 0.03 | hedged possibility 0.88 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We introduce a holomorphic representation for the Lorentzian EPRL spinfoam on arbitrary 2-complexes. The representation is obtained via the Ashtekar-Lewandowski-Marolf-Mour\~ao-Thiemann heat kernel coherent state transform. The new variables are classical holonomy-flux phase space variables $(h,X)\simeq \mathcal T^*SU(2)$ of Hamiltonian loop quantum gravity prescribing the holonomies of the Ashtekar connection $A=\Gamma + \gamma K$, and their conjugate gravitational fluxes. For small heat kernel `time' the spinfoam amplitude is peaked on classical space-time geometries, where at most countably many curvatures are allowed for non-zero Barbero-Immirzi parameter. We briefly comment on the possibility to use the alternative flipped classical limit.
Human review
How the literature uses it
10 arXiv papers cite this in 14 sentences
Papers citing it · 12 sentences without a confident label
Cites it as support 2 papers
-
The results produced by this code provide important pieces of evidence for resolving the confusion in the LQG community known as “the flatness problem” [ref] .
Spinfoams and high performance computing · Introduction · 0.96
-
One can extend the saddle point approximation to include the sums over the spins associated with an internal face, and this has been shown to imply that, in the limit of large boundary spins, the theory on a fixed cell-complex is dominated by flat solutions only [ref] .
Spinfoams: Foundations · Large spin asymptotics · 0.97
What it cites · 32 sentences without a confident label
Builds on 3 papers
-
In this paper we study the Segal-Bargmann coherent state transform of a local $SU(2)$ holonomy formulation of the EPRL Lorentzian spinfoam model [ref] , extending a previous analysis [ref] to an arbitrary number of vertices.
LQG vertex with finite Immirzi parameter · Introduction · 0.95
-
In this paper we study the Segal-Bargmann coherent state transform of a local $SU(2)$ holonomy formulation of the EPRL Lorentzian spinfoam model [ref] , extending a previous analysis [ref] to an arbitrary number of vertices.
Spinfoams in the holomorphic representation · Introduction · 0.95
-
The following theorem is a straightforward generalization to Lorentzian signature of the original theorem [ref] for the Euclidean case.
Relativistic spin networks and quantum gravity · A special case: the 4-simplex · 1.00
Uses the method or tool of 5 papers
-
The tools used for the proofs are a cocktail of the following techniques: Nottingham asymptotic techniques [ref] , graviton propagator techniques [ref] , and the semiclassical analysis of Hall coherent states [ref] .
LQG propagator from the new spin foams · Introduction · 1.00
-
The tools used for the proofs are a cocktail of the following techniques: Nottingham asymptotic techniques [ref] , graviton propagator techniques [ref] , and the semiclassical analysis of Hall coherent states [ref] .
Lorentzian spin foam amplitudes: graphical calculus and asymptotics · Introduction · 1.00
-
The tools used for the proofs are a cocktail of the following techniques: Nottingham asymptotic techniques [ref] , graviton propagator techniques [ref] , and the semiclassical analysis of Hall coherent states [ref] .
Coherent spin-networks · Introduction · 1.00
Compares with 3 papers
-
In fact, it is analogous to the `flatness constraint' agued in the spin-intertwiner spinfoam representation in [ref] , here analyzed in detail in terms of classical geometric variables thanks to the new holomorphic representation.
Spin foam models for quantum gravity from lattice path integrals · The face amplitude: connecting vertices · 0.92
-
Our analysis of the holomorphic Lorentzian amplitude at large areas provides a result which is compatible with the recent microlocal analysis of the Euclidean model [ref] .
Geometric asymptotics for spin foam lattice gauge gravity on arbitrary triangulations · Introduction · 0.94
-
Finally, we observe that the strictly positive case $β>0$ considered here is the same of reference [ref] .
Coherent spin-networks · The semiclassicality parameter $t$ · 0.85
Cites as support 2 papers
-
Indeed preliminary analyses [ref] suggest that the limit $γ→0$ could be used similarly to a semiclassical expansion, yielding non-trivial deficit angles.
Regge gravity from spinfoams · Conclusions · 0.96
-
Indeed preliminary analyses [ref] suggest that the limit $γ→0$ could be used similarly to a semiclassical expansion, yielding non-trivial deficit angles.
Emergence of gravity from spinfoams · Conclusions · 0.96
Cites as background 22 papers
-
We review some well-know results [ref] on the peakedness properties of the loop quantum gravity coherent states, in particular the computation of the expectation values of some geometric operators on coherent states, and their dispersions in the semiclassical limit.
Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties · The semiclassicality parameter $t$ · 0.99
-
We review some well-know results [ref] on the peakedness properties of the loop quantum gravity coherent states, in particular the computation of the expectation values of some geometric operators on coherent states, and their dispersions in the semiclassical limit.
Coherent spin-networks · The semiclassicality parameter $t$ · 0.99
-
The most common found in the literature is the spin-intertwiner coloring, but other equivalent variables revealed to be useful, such as holonomies [ref] and fluxes [ref] .
Local spin foams · SU(2) holonomy amplitude · 0.90
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.