Semi-Classical Limits of Simplicial Quantum Gravity

J.W. Barrett; T.J. Foxon

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Semi-Classical Limits of Simplicial Quantum Gravity

J.W. Barrett, T.J. Foxon

General Relativity and Quantum Cosmology · Submitted 8 Oct 1993

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

The authors' main claim This lends weight to the interpretation of the state-sum as a path integral, which has solutions corresponding to both Lorentzian and Euclidean gravity in three dimensions.

how it is stated · hedged possibility 0.76 read the record →

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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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,298 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.88 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We consider the simplicial state-sum model of Ponzano and Regge as a path integral for quantum gravity in three dimensions. We examine the Lorentzian geometry of a single 3-simplex and of a simplicial manifold, and interpret an asymptotic formula for $6j$-symbols in terms of this geometry. This extends Ponzano and Regge's similar interpretation for Euclidean geometry. We give a geometric interpretation of the stationary points of this state-sum, by showing that, at these points, the simplicial manifold may be mapped locally into flat Lorentzian or Euclidean space. This lends weight to the interpretation of the state-sum as a path integral, which has solutions corresponding to both Lorentzian and Euclidean gravity in three dimensions.

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	We consider the simplicial state-sum model of Ponzano and Regge as a path integral for quantum gravity in three dimensions.	background 0.59	0.45	0.04	asserted 0.97
s1	We examine the Lorentzian geometry of a single 3-simplex and of a simplicial manifold, and interpret an asymptotic formula for $6j$-symbols in terms of this geometry.	contribution 0.94	0.93	0.10	asserted 0.98
s2	This extends Ponzano and Regge's similar interpretation for Euclidean geometry.	contribution 0.46	0.49	0.06	asserted 0.99
s3	We give a geometric interpretation of the stationary points of this state-sum, by showing that, at these points, the simplicial manifold may be mapped locally into flat Lorentzian or Euclidean space.	result 0.73	0.94	0.37	asserted 0.68
s4	This lends weight to the interpretation of the state-sum as a path integral, which has solutions corresponding to both Lorentzian and Euclidean gravity in three dimensions.	interpretation 1.00	0.62	0.60	hedged possibility 0.76

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

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The paper

Original abstract

We consider the simplicial state-sum model of Ponzano and Regge as a path integral for quantum gravity in three dimensions. We examine the Lorentzian geometry of a single 3-simplex and of a simplicial manifold, and interpret an asymptotic formula for $6j$-symbols in terms of this geometry. This extends Ponzano and Regge's similar interpretation for Euclidean geometry. We give a geometric interpretation of the stationary points of this state-sum, by showing that, at these points, the simplicial manifold may be mapped locally into flat Lorentzian or Euclidean space. This lends weight to the interpretation of the state-sum as a path integral, which has solutions corresponding to both Lorentzian and Euclidean gravity in three dimensions.

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References

Forward citations

Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 66 citations worldwide. Full citation record

Causal structure and light-conical singularities in Lorentzian simplicial quantum gravity
gr-qc 2026-08 conditional novelty 7.0 of 10

Light-conical singularities dominate random Lorentzian Regge geometries, with trouser-type irregularities entropically preferred for bones shared by many 4-simplices.
Quantum geometry from higher gauge theory
gr-qc 2019-08 conditional novelty 7.0 of 10

The BFCG-Yetter model and the KBF state sum produce the same single-4-simplex amplitude when evaluated on boundary states called G-networks.
(2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality
gr-qc 2024-11 conditional novelty 6.0 of 10

A 2+1 Lorentzian spin-foam cosmology model with a Hessian-derived measure and a massive scalar field yields convergent partition functions, with semi-classical expectation values only in the causally regular sector an...
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.
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...

Show 3 more citing papers

Causal structure in spin-foams
gr-qc 2021-09 unverdicted novelty 5.0 of 10

Proposes a causal EPRL spin-foam model where the two-complex orientation encodes causality and aids semiclassical geometry reconstruction.
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.

How the literature uses it

21 arXiv papers cite this in 25 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 · 14 sentences without a confident label

Builds on it 3 papers

For the Lorentzian case, we generalize a definition given by Barrett and Foxon [ref] for $1+1$ dimensional Minkowski space and we clarify certain aspects of the construction which are important for applications in spin foams and which are a common source of confusion.

Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity · On Euclidean and Lorentzian Angles · 0.99
In this section we address this question within the general framework of this paper, replacing at each simplex in the Regge path integral the exponential of the action by its spinfoam-inspired equivalent, and showing that the contribution from the non-Regge terms is suppressed in the semiclassical limit[This can be seen as a continuation and generalization of the work done in [ref] for the Ponzano-Regge model in 3d.

Semiclassical regime of Regge calculus and spin foams · Semiclassical regime of spin foam models · 0.98
Extending the formulae of [ref] to the $4$-dimensional case, the lorentzian Regge action is a sum over the triangles $t$: [equation] with $A_t$ the area of the triangle $t$, and $δ_t$ the deficit angle defined as a sum over the 4-simplices $σ$ surrounding $t$: [equation] with the dihedral angle defined by equation [ref].

Causal structure in spin-foams · Lorentzian Regge calculus · 0.96

Uses its method or tool 1 paper

For such Lorentzian boundary data, we have followed [ref] and defined the 4d dihedral angles $þ_a1$ as [equation] The choice of sign for $þ_a1$ is purely conventional, and it is made to simplify the parametrization of the solutions.

Asymptotics of lowest unitary SL(2,C) invariants on graphs · Lorentzian solutions · 0.86

Compares with it 1 paper

However here what we get is a generalized Regge action, in the sense of Barrett and Foxon [ref] , a situation similar to the Ponzano-Regge model for spinfoam gravity in three spacetime dimensions [ref] .

Regge gravity from spinfoams · The continuum $γ→0$ limit · 0.88

Cites it as support 2 papers

Indeed, the spin foam path integral, which results from a connection representation of general relativity, includes contributions from such Euclidean simplices [ref] .

Lorentzian quantum cosmology goes simplicial · Discretisation with one 4-polytope · 0.98
* the path integral includes quantum tunnelling through Lorentzian geometries; this exponentially-suppressed geometries come from tetrahedra with negative Cayley determinant, in which case they can not be embedded in a Euclidean signature but are naturally Lorentzian objects [ref] ; this allows quantum transition through changes of space-time signature.

Spinfoam Models for Quantum Gravity: Overview · 3d Quantum Gravity · 0.97

Cites it as background 2 papers

First formulated in terms of the magnetic basis [ref] , a coherent-state representation of the (2+1) model has been developed recently in [ref] .

(2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality · A cuboidal spin-foam amplitude for Lorentzian gravity · 0.88
Einstein-Regge action is a discretization of Einstein-Hilbert action of gravity $𝐒_EH=∫__4(R-2κ)+∫_∂_4 K$ using constant curvature 4-simplices [ref] .

4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block · Holomorphic Block and 4-dimensional Quantum Geometry · 0.81

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