Euclidean and Lorentzian quantum gravity -- lessons from two dimensions
type: Item
instance of: scholarly article
title: Euclidean and Lorentzian quantum gravity -- lessons from two dimensions
zbMATH Open document ID: 1005.83015
DOI: 10.1016/S0960-0779(98)00197-0
author: J. L. Nielsen
author: J. Rolf
author: Jan Ambjørn
author: Renate Loll
published in: Chaos, Solitons and Fractals
publication date: 2002-08-18T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/9806241
review text: In this article some recent progress in understanding of two-dimensional quantum gravity is reviewed. In particular, the relation between the Euclidean and Lorentzian sectors of the quantum theory are discussed. It is shown that it is indeed possible to formulate a background-independent theory of quantum gravity and still maintain some analogues of concepts from classical gravity. This holds true at least in the case of one-plus-one dimensional gravity. The authors show that the generic two-dimensional geometry is fractal with intrinsic Hausdorff dimension four. They conclude that this situation is reminiscent of the random walk representation for a free particle. The authors also discuss the relation between Euclidean quantum gravity, defined via a non-pertubative path integral, and a similar construction in the Lorentzian case. In the latter case they obtain a continuum limit different from that of Euclidean quantum gravity. The authors conclude that this difference can be traced to the presence or absence of topology changes of space. In fact, it is shown that an agreement with the theory of Euclidean quantum gravity can only be obtained when spatial topology changes are allowed.
reviewed by: Jürgen Tolksdorf
Mathematics Subject Classification ID: 83C45
Mathematics Subject Classification ID: 83C80
zbMATH DE Number: 1783116
zbMATH Keywords: quantum gravity
zbMATH Keywords: two dimensions
zbMATH Keywords: path integral
zbMATH Keywords: topology changes
MaRDI profile type: Publication
arXiv ID: hep-th/9806241
cites work: Non-perturbative Lorentzian quantum gravity, causality and topology change
cites work: The spectral dimension of \(2\)D quantum gravity
cites work: Scaling in quantum gravity
cites work: On the fractal structure of two-dimensional quantum gravity
cites work: Quantum gravity and random surfaces
OpenAlex ID: W2149052153
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