Quantization and the Issue of Time for Various Two-Dimensional Models of Gravity

Details Quantization and the Issue of Time for Various Two-Dimensional Models of Gravity Quantization and the Issue of Time for Various Two-Dimensional Models of Gravity

1993-08-31

arxiv.org/abs/hep-th/9308155v1

Int.J.Mod.Phys.D3:281-284,1994

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, LaTeX, Talk given at the Journ\'ees Relativistes '93, TUW9309

Scientific paper

10.1142/S0218271894000460

It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and $R^2$-Gravity are {\em embedded} in the Katanaev-Volovich model of 2D NonEinsteinian Gravity. Different approaches to the formulation of a quantum theory for the above systems are then presented: The Dirac constraints can be solved exactly in the momentum representation, the path integral can be integrated out, and the constraint algebra can be {\em explicitely} canonically abelianized, thus allowing also for a (superficial) reduced phase space quantization. Non--trivial dynamics are obtained by means of time dependent gauges. All of these approaches lead to the {\em same} finite dimensional quantum mechanical system.

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