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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2000-1
January 2000

On the relation between Euclidean and Lorentzian 2D quantum gravity


Jan Ambjørn

J. Correia, C. Kristjansen, R. Loll


Starting from 2D Euclidean quantum gravity, we show that one recovers 2D Lorentzian quantum gravity by removing all baby universes. Using a peeling procedure to decompose the discrete, triangulated geometries along a one-dimensional path, we explicitly associate with each Euclidean space-time a (generalized) Lorentzian space-time. This motivates a map between the parameter spaces of the two theories, under which their propagators get identified. In two dimensions, Lorentzian quantum gravity can therefore be viewed as a 'renormalized' version of Euclidean quantum gravity.

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This paper has now been published in Phys. Lett. B 475 (2000), no. 1-2, 24--32