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Cited by 232Noncommutative and Quantum Gravity TheoriesRelativity and Gravitational TheoryBlack Holes and Theoretical Physics

Discrete Approaches to Quantum Gravity in Four Dimensions

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Loll, Renate·1998·Living Reviews in Relativity
DOI 10.12942/lrr-1998-13PMC PMC5253799
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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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  • Dynamical triangulation has been proven useful in two-dimensional gravity, and important steps have been taken in higher dimensions, especially with recent progress in understanding Lorentzian triangulations.

    “Dynamical triangulation has been proven to be quite useful in two-dimensional gravity, and some important steps have been taken in higher dimensions, especially with the recent progress in understanding Lorentzian triangulations.”

    From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [179]

    The Dynamical triangulations Introduction calls the method a valuable tool in two-dimensional gravity, and the Summary describes results from four-dimensional simulations. The paper does not report recent progress in understanding Lorentzian triangulations; its Conclusions and Outlook instead call continuation of path-integral results to Lorentzian signature an unresolved problem. No page numbers are available in our copy. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

  • For ordinary Euclidean dynamical triangulations, few signs of a continuum limit have been seen; the system appears to exhibit two phases-a crumpled phase with extremely large Hausdorff dimension and a branched polymer phase-neither of which look much like a classical spacetime.

    “For ordinary “Euclidean” dynamical triangulations, few signs of such a continuum limit have been seen. The system appears to exhibit two phases — a “crumpled” phase, in which the Hausdorff dimension is extremely large, and a “branched polymer” phase — neither of which look much like a classical spacetime [179].”

    From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [179]

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Cited by

Sorted by citations

Authors
Loll, R.
Affiliations
Max Planck Institute for Gravitational Physics (DE)
Corresponding author
Loll, Renate
ORCID
Loll, Renate
Venue
Living Reviews in Relativity
Publisher
Springer Science and Business Media LLC
Published
1998-12
Volume
1
Issue
1
Pages
13-13
ISSN
  • 1433-8351 (ISSN-L)
  • 2367-3613
DOI
10.12942/lrr-1998-13
PMC
PMC5253799
OpenAlex
W2168251042
Cited by
232
References
5
Citations by year
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FWCI
0.94
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • Living Reviews in Relativity (publishedVersion, cc-by)
  • PubMed Central (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • Utrecht University Repository (Utrecht University) (submittedVersion, other-oa)
  • Max Planck Institute for Plasma Physics (submittedVersion)
  • Max Planck Digital Library (submittedVersion)
  • MPG.PuRe (Max Planck Society) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
Keywords
quantum gravity, discrete spacetime, path integral, Hamiltonian formulation, dynamical triangulations, four-dimensional gravity

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