Lorentzian LQG vertex amplitude

Roberto Pereira

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Lorentzian LQG vertex amplitude

Roberto Pereira

General Relativity and Quantum Cosmology · Submitted 26 Oct 2007

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

The authors' main claim The main features of the Euclidean model are preserved in the Lorentzian one.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.89 · mentions code or data availability 0.02.

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We generalize a model recently proposed for Euclidean quantum gravity to the case of Lorentzian signature. The main features of the Euclidean model are preserved in the Lorentzian one. In particular, the boundary Hilbert space matches the one of SU(2) loop quantum gravity. As in the Euclidean case, the model can be obtained from the Lorentzian Barrett-Crane model from a flipping of the Poisson structure, or alternatively, by adding a topological term to the action and taking the small Barbero-Immirzi parameter limit.

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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	We generalize a model recently proposed for Euclidean quantum gravity to the case of Lorentzian signature.	contribution 1.00	0.92	0.19	asserted 0.99
s1	The main features of the Euclidean model are preserved in the Lorentzian one.	result 0.89	0.76	0.28	asserted 1.00
s2	In particular, the boundary Hilbert space matches the one of SU(2) loop quantum gravity.	result 0.99	0.72	0.19	asserted 1.00
s3	As in the Euclidean case, the model can be obtained from the Lorentzian Barrett-Crane model from a flipping of the Poisson structure, or alternatively, by adding a topological term to the action and taking the small Barbero-Immirzi parameter limit.	method 0.87	0.55	0.15	asserted 0.94

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.94.

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arXiv listing abstract v2

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S sections
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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

The paper

Original abstract

We generalize a model recently proposed for Euclidean quantum gravity to the case of Lorentzian signature. The main features of the Euclidean model are preserved in the Lorentzian one. In particular, the boundary Hilbert space matches the one of SU(2) loop quantum gravity. As in the Euclidean case, the model can be obtained from the Lorentzian Barrett-Crane model from a flipping of the Poisson structure, or alternatively, by adding a topological term to the action and taking the small Barbero-Immirzi parameter limit.

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References

Forward citations

Cited by 6 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.
LQG vertex with finite Immirzi parameter
gr-qc 2007-11 conditional novelty 7.0 of 10

Imposing the simplicity constraints on a finite-Immirzi-parameter spinfoam vertex yields a boundary Hilbert space and area spectrum identical to loop quantum gravity, in both Euclidean and Lorentzian signatures.
Lorentzian spin foam amplitudes: graphical calculus and asymptotics
gr-qc 2009-07 conditional novelty 6.0 of 10

In the large-spin limit the Lorentzian EPRL four-simplex amplitude oscillates with phase equal to plus or minus the Immirzi-scaled Lorentzian Regge action, and the proportionality of the two representation labels is f...
On the semiclassical limit of 4d spin foam models
gr-qc 2008-09 conditional novelty 6.0 of 10

In the large-spin limit the FK-gamma spin foam amplitude on an arbitrary triangulation is exponentially suppressed unless the face spins come from a discrete geometry, in which case it reduces to exp(i times the Regge...
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.

Show 1 more citing papers

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.

How the literature uses it

29 arXiv papers cite this in 53 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 · 40 sentences without a confident label

Builds on it 1 paper

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] .

Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory · Physical boundary Hilbert space of the new theory · 0.80

Uses its method or tool 2 papers

We evaluate it in the basis of the coherent states [ref] , so that the expression $⟨A | ψ_H_ℓ ⟩=W(H_ℓ)$ reads [equation] The amplitude is Lorentzian, with an integration over the $(2,)$ elements $G_n$ associated to the edges (see Fig. [ref]).

Learning about Quantum Gravity with a Couple of Nodes · Vertex amplitude · 0.92
We use the version of the amplitude developed in [ref] generally denoted as the EPRL amplitude.

Numerical analysis of the self-energy in covariant Loop Quantum Gravity · Introduction · 0.80

Compares with it 1 paper

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).

Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory · Introduction · 0.83

Cites it as background 8 papers

Here, we briefly describe in Section II the discrete theory introduced in [ref] (euclidean case) and in [ref] (lorentzian case), in order to make this paper self contained.

LQG vertex with finite Immirzi parameter · Introduction · 0.91
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
In particular, a vertex amplitude $A_v(j_f,i_e)$ that might define a quantum theory of gravity has been developed in [ref] and is today under intense investigation (see [ref] ).

Face amplitude of spinfoam quantum gravity · Introduction · 0.95

What it cites · 12 sentences without a confident label

Builds on 1 paper

In [ref] only the Euclidean signature case was considered.

Flipped spinfoam vertex and loop gravity · Introduction · 0.80

Uses the method or tool of 1 paper

We follow the strategy in [ref] and impose $M_f:=(C_f^i)^2≈0$, allowing at the same time for possible corrections, small in the semiclassical limit.

Flipped spinfoam vertex and loop gravity · Quantization and vertex amplitude · 0.99

Compares with 2 papers

(iii) Finally, the model defined here is clearly distinct from other models proposed in the literature as alternatives to the Barrett-Crane model [ref] , as it is based solely on the simple representations of the form $(n,0)$.

A New Spin Foam Model for 4d Gravity · Conclusion · 1.00
(iii) Finally, the model defined here is clearly distinct from other models proposed in the literature as alternatives to the Barrett-Crane model [ref] , as it is based solely on the simple representations of the form $(n,0)$.

Spin foam model from canonical quantization · Conclusion · 1.00

Cites as support 1 paper

As argued in [ref] the problem can be traced back to the way some of the constraints are imposed in the Barrett-Crane model.

Flipped spinfoam vertex and loop gravity · Introduction · 0.98

Cites as background 3 papers

Spin foam techniques [ref] have been developed as a possible framework to study the quantum dynamics.

A lattice worldsheet sum for 4-d Euclidean general relativity · Introduction · 0.98
Loop quantum gravity (LQG) [ref] provides a well defined, background independent, construction of the kinematical Hilbert space of quantum general relativity.

An Introduction to Loop Quantum Gravity Through Cosmology · Introduction · 0.99
Matters of triangulation independence could be adressed by a group field theory [ref] approach.

The group field theory approach to quantum gravity · Introduction · 0.80

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