Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory

Carlo Rovelli; You Ding

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Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory

You Ding, Carlo Rovelli

General Relativity and Quantum Cosmology · Submitted 7 Jun 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The vanishing is exact (and not just in the large quantum number limit.) We also generalize the definition of the volume operator in the spinfoam model to the Lorentzian signature, and show that it matches the one of loop quantum gravity, as does in the Euclidean case.

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arXiv ID1006.1294 (version 3)

Pith IDYBBEY7AH, Pith's permanent record of this paper and its review

CitationCarlo Rovelli, You Ding. "Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory." arXiv:1006.1294 (2010). https://pith.science/paper/YBBEY7AH

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.88 · mentions code or data availability 0.02.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the constraints that defines the model. We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU(2) representations into the SL(2,C) ones. We then show directly that all constraints vanish on this space in a weak sense. The vanishing is exact (and not just in the large quantum number limit.) We also generalize the definition of the volume operator in the spinfoam model to the Lorentzian signature, and show that it matches the one of loop quantum gravity, as does in the Euclidean case.

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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	A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity.	background 1.00	0.07	0.03	asserted 0.52
s1	In this paper we reconsider the implementation of the constraints that defines the model.	contribution 0.80	0.68	0.03	asserted 0.58
s2	We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU(2) representations into the SL(2,C) ones.	contribution 0.57	0.96	0.08	asserted 1.00
s3	We then show directly that all constraints vanish on this space in a weak sense.	result 0.99	0.95	0.29	asserted 1.00
s4	The vanishing is exact (and not just in the large quantum number limit.) We also generalize the definition of the volume operator in the spinfoam model to the Lorentzian signature, and show that it matches the one of loop quantum gravity, as does in the Euclidean case.	result 0.82	0.95	0.54	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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full text
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Original abstract

A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the constraints that defines the model. We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU(2) representations into the SL(2,C) ones. We then show directly that all constraints vanish on this space in a weak sense. The vanishing is exact (and not just in the large quantum number limit.) We also generalize the definition of the volume operator in the spinfoam model to the Lorentzian signature, and show that it matches the one of loop quantum gravity, as does in the Euclidean case.

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References

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Edge modes of gravity. Part III. Corner simplicity constraints
hep-th 2020-07 conditional novelty 7.0 of 10

The corner area element equals the Poincaré spin Casimir, and the continuum simplicity constraints split into two second class and one first class component, leaving the full Lorentz algebra as Dirac observables.
The continuum limit of loop quantum gravity - a framework for solving the theory
gr-qc 2014-09 accept novelty 3.0 of 10

The paper argues that the continuum limit of loop quantum gravity is equivalent to the physical Hilbert space and sketches an iterative coarse-graining program, with diffeomorphism symmetry as the indicator that the l...
Les Houches lectures on Spinfoam Path Integrals
gr-qc 2026-07 accept novelty 2.0 of 10

A pedagogical review of spinfoam path integrals, from 1d quantum mechanics and 2d BF theory through Ponzano-Regge/Turaev-Viro to the 4d EPRL model, accurate but with no new results.
The Spin Foam Approach to Quantum Gravity
gr-qc 2012-05 accept novelty 2.0 of 10

The review presents the spin foam quantization of gravity as a constrained BF path integral, focusing on the EPRL and Freidel-Krasnov models and on 2+1 gravity as a solvable guide.
Zakopane lectures on loop gravity
gr-qc 2011-02 accept novelty 2.0 of 10

Loop quantum gravity is presented as a covariant framework in which discrete spin-network quanta of space evolve through spinfoam amplitudes whose semiclassical limit is claimed to reproduce general relativity.

How the literature uses it

20 arXiv papers cite this in 35 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 · 29 sentences without a confident label

Builds on it 1 paper

In a path integral framework, the EPRL spinfoam amplitudes [ref] are straightforward to adapt to this new setting with relaxed area matching along spin network edges by projected onto different spins at the ends of every edges as suggested in [ref] .

Area Propagator and Boosted Spin Networks in Loop Quantum Gravity · Conclusion & Outlook · 0.95

Cites it as support 2 papers

In fact, not only the states are identified, but there is also a way of defining quantum operators of area and volume in the spin foam context such that their spectra coincide with those of the canonical quantization [ref] .

Spin Foams and Canonical Quantization · Identification of kinematical states · 1.00
Moreover, geometric operators such as volume and area defined in the covariant context are shown to coincide with the corresponding operators defined in the canonical formulation [ref] .

The Spin Foam Approach to Quantum Gravity · Boundary Data for the New Models and Relationship with the Canonical Theory · 0.99

Cites it as background 3 papers

Currently one of the successful spin foam models is the EPRL/FK model defined in [ref] , whose implementation of simplicity constraint is understood in the sense of [ref] .

Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory · Introduction · 0.90
One can identify two types of studies: One involving canonical analysis and weak imposition of the constraints [ref] and another one involving the use of coherent states [ref] .

Edge modes of gravity. Part III. Corner simplicity constraints · Algebra of simplicity constraints · 0.98
A very important topic that will be left out are the new insights regarding how the 3d and the 4d picture can come together [ref] , [ref] , [ref] .

New insights in quantum geometry · Introduction · 0.98

What it cites · 57 sentences without a confident label

Builds on 2 papers

In this section, we use the matrix element approach to construct the physical boundary Hilbert space of the new spin-foam theory with Lorentzian signature [ref] .

Lorentzian LQG vertex amplitude · Physical boundary Hilbert space of the new theory · 0.80
In this section, we use the matrix element approach to construct the physical boundary Hilbert space of the new spin-foam theory with Lorentzian signature [ref] .

LQG vertex with finite Immirzi parameter · Physical boundary Hilbert space of the new theory · 0.80

Compares with 4 papers

The model we construct contains in fact a slight modification with respect to the one in [ref] (corresponding to a slightly different factor ordering of the constraints).

The loop-quantum-gravity vertex-amplitude · Introduction · 0.83
The model we construct contains in fact a slight modification with respect to the one in [ref] (corresponding to a slightly different factor ordering of the constraints).

Flipped spinfoam vertex and loop gravity · Introduction · 0.83
The model we construct contains in fact a slight modification with respect to the one in [ref] (corresponding to a slightly different factor ordering of the constraints).

Lorentzian LQG vertex amplitude · Introduction · 0.83

Cites as background 6 papers

The spinfoam formalism [ref] and canonical loop quantum gravity (LQG) [ref] can ideally be viewed as the covariant and the canonical versions, respectively, of a background-independent quantum theory of gravity [ref] .

A new look at loop quantum gravity · Introduction · 0.99
The spinfoam formalism [ref] and canonical loop quantum gravity (LQG) [ref] can ideally be viewed as the covariant and the canonical versions, respectively, of a background-independent quantum theory of gravity [ref] .

An Introduction to Loop Quantum Gravity Through Cosmology · Introduction · 0.99
The spinfoam formalism [ref] and canonical loop quantum gravity (LQG) [ref] can ideally be viewed as the covariant and the canonical versions, respectively, of a background-independent quantum theory of gravity [ref] .

Worldsheet formulations of gauge theories and gravity · Introduction · 0.99

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