Recent Progress in Regge Calculus

Ruth M. Williams

RECORD

Recent Progress in Regge Calculus

Ruth M. Williams

General Relativity and Quantum Cosmology · Submitted 3 Feb 1997

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

The authors' main claim For the three-sphere and the three-torus, the numerical results agree with the analytic ones and show the existence of degeneracy and signature change.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

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

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,782 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.27 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.65 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

While there has been some advance in the use of Regge calculus as a tool in numerical relativity, the main progress in Regge calculus recently has been in quantum gravity. After a brief discussion of this progress, attention is focussed on two particular, related aspects. Firstly, the possible definitions of diffeomorphisms or gauge transformations in Regge calculus are examined and examples are given. Secondly, an investigation of the signature of the simplicial supermetric is described. This is the Lund-Regge metric on simplicial configuration space and defines the distance between simplicial three-geometries. Information on its signature can be used to extend the rather limited results on the signature of the supermetric in the continuum case. This information is obtained by a combination of analytic and numerical techniques. For the three-sphere and the three-torus, the numerical results agree with the analytic ones and show the existence of degeneracy and signature change. Some ``vertical'' directions in simplicial configuration space, corresponding to simplicial metrics related by gauge transformations, are found for the three-torus.

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	While there has been some advance in the use of Regge calculus as a tool in numerical relativity, the main progress in Regge calculus recently has been in quantum gravity.	background 1.00	0.05	0.28	asserted 1.00
s1	After a brief discussion of this progress, attention is focussed on two particular, related aspects.	background 0.48	0.13	0.04	unclear 0.54
s2	Firstly, the possible definitions of diffeomorphisms or gauge transformations in Regge calculus are examined and examples are given.	contribution 0.99	0.67	0.04	asserted 0.68
s3	Secondly, an investigation of the signature of the simplicial supermetric is described.	contribution 0.99	0.73	0.04	asserted 0.74
s4	This is the Lund-Regge metric on simplicial configuration space and defines the distance between simplicial three-geometries.	background 0.78	0.15	0.07	asserted 1.00
s5	Information on its signature can be used to extend the rather limited results on the signature of the supermetric in the continuum case.	interpretation 0.67	0.42	0.09	asserted 0.52
s6	This information is obtained by a combination of analytic and numerical techniques.	method 1.00	0.73	0.03	asserted 0.99
s7	For the three-sphere and the three-torus, the numerical results agree with the analytic ones and show the existence of degeneracy and signature change.	result 1.00	0.86	0.26	asserted 1.00
s8	Some ``vertical'' directions in simplicial configuration space, corresponding to simplicial metrics related by gauge transformations, are found for the three-torus.	result 1.00	0.88	0.14	asserted 1.00

What kind of paper the classifier reports this is: review 0.64 · evidence from simulation or computation 0.78.

What was examined, and what was not

sources read

arXiv listing abstract v1

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

The paper

Original abstract

While there has been some advance in the use of Regge calculus as a tool in numerical relativity, the main progress in Regge calculus recently has been in quantum gravity. After a brief discussion of this progress, attention is focussed on two particular, related aspects. Firstly, the possible definitions of diffeomorphisms or gauge transformations in Regge calculus are examined and examples are given. Secondly, an investigation of the signature of the simplicial supermetric is described. This is the Lund-Regge metric on simplicial configuration space and defines the distance between simplicial three-geometries. Information on its signature can be used to extend the rather limited results on the signature of the supermetric in the continuum case. This information is obtained by a combination of analytic and numerical techniques. For the three-sphere and the three-torus, the numerical results agree with the analytic ones and show the existence of degeneracy and signature change. Some ``vertical'' directions in simplicial configuration space, corresponding to simplicial metrics related by gauge transformations, are found for the three-torus.

Human review

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

References

Forward citations

Cited by 8 Pith papers

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

Canonical simplicial gravity
gr-qc 2011-08 conditional novelty 7.0 of 10

A canonical formalism built on Hamilton's principal function implements Pachner moves as canonical transformations, giving a consistent Hamiltonian evolution for Regge calculus with changing lattice size.
Effective Spin Foam Models for Four-Dimensional Quantum Gravity
gr-qc 2020-04 conditional novelty 6.0 of 10

A family of simplified spin foam models keeps the discrete area spectrum while imposing gluing constraints only as strongly as quantum uncertainty permits, and curvature is not suppressed provided the combination gamm...
Path integral measure and triangulation independence in discrete gravity
gr-qc 2011-10 accept novelty 6.0 of 10

A local path integral measure for linearized 3D Regge calculus makes the amplitude triangulation independent and reproduces the Ponzano-Regge asymptotics; in 4D only partial invariance survives.
From covariant to canonical formulations of discrete gravity
gr-qc 2009-12 conditional novelty 6.0 of 10

Canonical constraints for linearized Regge calculus on a flat background are derived directly from the discrete action and shown to be local, first class and Abelian, while at quadratic order they become gauge-depende...
Improved and Perfect Actions in Discrete Gravity
gr-qc 2009-07 conditional novelty 6.0 of 10

In three dimensions with a cosmological constant, the perfect action of Regge calculus is the Regge action of constantly curved tetrahedra whose curvature equals the cosmological constant, and it restores the vertex d...

Show 3 more citing papers

Dynamically Triangulating Lorentzian Quantum Gravity
hep-th 2001-05 conditional novelty 6.0 of 10

A complete technical construction of Lorentzian dynamical triangulations in 3 and 4 dimensions, with a non-perturbative Wick rotation, a self-adjoint Hamiltonian from the squared transfer matrix, and kinematic bounds ...
Diffeomorphism symmetry in quantum gravity models
gr-qc 2008-10 conditional novelty 3.0 of 10

Discretized quantum gravity must preserve exact symmetries at flat vertices and track approximate ones elsewhere, in both the action and the canonical constraints, or the continuum limit will be wrong.
Discrete Gravity Models and Loop Quantum Gravity: a Short Review
gr-qc 2012-04 conditional novelty 2.0 of 10

Loop quantum gravity on a fixed graph describes twisted geometries, a generalization of Regge calculus that reduces to Regge geometries when shape-matching conditions are imposed.

How the literature uses it

12 arXiv papers cite this in 18 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 · 4 sentences without a confident label

Cites it as support 1 paper

Instead of trying to define what the equivalent of a continuous diffeomorphism might be for a discrete manifold, we will take the Regge action and hence the discrete system it describes as fundamental and just ask for symmetries of this action, as is advocated for instance by Williams [ref] .

Diffeomorphism symmetry in quantum gravity models · Bianchi identities and symmetries of the Regge action · 0.97

Cites it as background 10 papers

In this spirit, we shall attempt to explore the dynamics of Regge Calculus [ref] , the most well-known simplicial discretization of general relativity.

Canonical linearized Regge Calculus: counting lattice gravitons with Pachner moves · Introduction · 0.93
In this article, we will develop this evolution scheme for a particular discretization of general relativity, namely Regge calculus [ref] .

Canonical simplicial gravity · Regge calculus · 0.86
A natural discretization of General Relativity is achieved by Regge calculus, where the smooth space-time is replaced by a simplicial complex, and the metric information is contained in the edge lengths and deficit angles around the hinges [ref] .

Improved and Perfect Actions in Discrete Gravity · Introduction · 0.93

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.