A Phase Space Path Integral for (2+1)-Dimensional Gravity

TL;DR

This paper explores the connection between phase space path integrals and canonical quantization in (2+1)-dimensional gravity, establishing their equivalence and addressing key subtleties in the path integral formulation.

Contribution

It demonstrates the equivalence between phase space path integral and canonical quantization in (2+1)-D gravity, clarifying the necessary conditions for this correspondence.

Findings

Proves the equivalence of the two quantization approaches.

Identifies subtleties in defining the path integral.

Provides insights into (2+1)-D gravity quantization.

Abstract

I investigate the relationship between the phase space path integral in (2+1)-dimensional gravity and the canonical quantization of the corresponding reduced phase space in the York time slicing. I demonstrate the equivalence of these two approaches, and discuss some subtleties in the definition of the path integral necessary to prove this equivalence.