2d quantum dilaton gravity as/versus finite dimensional quantum mechanical systems

TL;DR

This paper explores the formulation and quantization of 2D quantum dilaton gravity, highlighting its connection to finite-dimensional quantum systems and discussing black hole entropy in this context.

Contribution

It introduces a Chern--Simons formulation of 2D dilaton gravity and analyzes its Hamiltonian quantization, emphasizing its relation to finite-dimensional quantum mechanical systems.

Findings

Establishes a link between 2D dilaton gravity and finite-dimensional quantum systems

Provides a Hamiltonian quantization framework for the theory

Discusses the statistical mechanical entropy of 2D black holes

Abstract

I present the ``Chern--Simons'' formulation of generalized 2d dilaton gravity, summarize its Hamiltonian quantization (reduced phase space and Dirac quantization) and briefly discuss the statistical mechanical entropy of 2d black holes. Focus is put on the close relation to finite dimensional point particle systems.