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  Euclidean and Lorentzian quantum gravity - lessons from two dimensions

Ambjörn, J., Nielsen, J. L., Rolf, J., & Loll, R. (1999). Euclidean and Lorentzian quantum gravity - lessons from two dimensions. Chaos, Solitons and Fractals, 10(2-3), 177-195. doi:10.1016/S0960-0779(98)00197-0.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5873-A Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5874-8
Genre: Journal Article

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Ambjörn, Jan, Author
Nielsen, J. L., Author
Rolf, J., Author
Loll, Renate1, Author
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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24014              

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 Abstract: No theory of four-dimensional quantum gravity exists as yet. In this situation the two-dimensional theory, which can be analyzed by conventional field-theoretical methods, can serve as a toy model for studying some aspects of quantum gravity. It represents one of the rare settings in a quantum-gravitational context where one can calculate quantities truly independent of any background geometry. We review recent progress in our understanding of 2d quantum gravity, and in particular the relation between the Euclidean and Lorentzian sectors of the quantum theory. We show that conventional 2d Euclidean quantum gravity can be obtained from Lorentzian quantum gravity by an analytic continuation only if we allow for spatial topology changes in the latter. Once this is done, one obtains a theory of quantum gravity where space-time is fractal: the intrinsic Hausdorff dimension of usual 2d Euclidean quantum gravity is four, and not two. However, certain aspects of quantum space-time remain two-dimensional, exemplified by the fact that its so-called spectral dimension is equal to two.

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 Dates: 1999
 Publication Status: Published in print
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 Identifiers: eDoc: 206119
Other: 16371
DOI: 10.1016/S0960-0779(98)00197-0
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Title: Chaos, Solitons and Fractals
Source Genre: Journal
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Pages: - Volume / Issue: 10 (2-3) Sequence Number: - Start / End Page: 177 - 195 Identifier: -