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

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.

4 pages, LaTeX, Talk given at the Journées Relativistes '93, TUW9309

Cited by in corpus (4)

• Classical and Quantum Gravity in 1+1 Dimensions, Part I: A Unifying Approach
• Dirac Quantization Gravity-Yang-Mills Systems in 1+1 Dimensions
• JT Gravity in de Sitter Space and the Problem of Time
• Aspects of Jackiw-Teitelboim Gravity in Anti-de Sitter and de Sitter spacetime