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

Thomas Strobl

doi:10.1142/s0218271894000460

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arXiv · hep-th/9308155

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

Thomas Strobl

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Abstract

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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Thomas Strobl. 1993-08-31. Quantization and the Issue of Time for Various Two-Dimensional Models of Gravity. https://doi.org/10.1142/s0218271894000460

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