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Discrete approaches to quantum gravity in four dimensions
General Relativity and Quantum Cosmology · Submitted 13 May 1998
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation, quantum Regge calculus, and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.
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The abstract, sentence by sentence
The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation, quantum Regge calculus, and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. | background 0.98 | 0.03 | 0.03 | asserted 1.00 |
| s1 | One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. | background 0.64 | 0.05 | 0.04 | hedged possibility 0.66 |
| s2 | I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation, quantum Regge calculus, and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature. | contribution 0.96 | 0.21 | 0.08 | asserted 0.82 |
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The paper
Original abstract
The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation, quantum Regge calculus, and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.
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References
How the literature uses it
52 arXiv papers cite this in 82 sentences
Papers citing it · 37 sentences without a confident label
Contests it 1 paper
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Claims of the presence of a second-order phase transition [ref] in the corresponding lattice quantum gravity model, so-called Euclidean dynamical triangulations (EDT) or DT for short, signalling the possible existence of a continuum limit, generated much attention at the time, but were later shown to be erroneous.[summaries of the set-up and results of EDT in four dimensions and further references can be found in [ref] ].
Nonperturbative quantum gravity unlocked through computation · Introduction · contest 0.76
Uses its method or tool 1 paper
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Firstly, one can use Markov chain Monte Carlo methods [ref] to approximate gravitational path integrals, usually regularized in terms of simplicial geometries, as is the case in the approaches of (causal) dynamical triangulations (see Q27 and [ref] ) and quantum Regge calculus (see Q26 and [ref] ).
Quantum Gravity in 30 Questions · Q16: Which technical tools are needed to make progress in quantum gravity? · 0.85
Compares with it 1 paper
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It is similar to Regge's [ref] approach but retains fixed coordination and is based on an internal symmetry.
Causal Space-Times on a Null Lattice · Summary and Discussion · 0.89
Cites it as support 1 paper
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Bad news has been confirmed by results (see [ref] , [ref] ) from numerical simulations.
Analysis of the Semiclassical Solution of CDT · EDT and their failure · 0.97
Cites it as background 34 papers
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CDT quantum gravity is a modern implementation of lattice gravity[see [ref] for an overview of earlier approaches], based on a nonperturbative, regularized path integral over piecewise flat (triangulated) manifolds (see [ref] for reviews).
Curvature profiles for quantum gravity · On the nature of quantum observables · 1.00
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The quantum theory is normally defined, for a given triangulation, by the path integral over all edge lengths in the triangulation[“Problem 57” in [ref] . ] [ref] : [equation] where $μ(l_i)$ is a suitable measure function [ref] and some fixed asymptotic boundary condition is understood.
Semiclassical regime of Regge calculus and spin foams · Regge calculus and boundary state · 0.93
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The question whether Regge gravity features a notion of diffeomorphism symmetry has been debated in the literature [ref] .
Spin foams, Refinement limit and Renormalization · The need for renormalization: restoring diffeomorphism symmetry · 0.89
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