Functional approach to 2+1 dimensional gravity coupled to particles

TL;DR

This paper develops a functional integral approach to quantum gravity in 2+1 dimensions with point particles, analyzing gauge choices, boundary terms, and the role of functional determinants, advancing understanding of lower-dimensional quantum gravity.

Contribution

It introduces a novel phase-space functional integral formulation for 2+1D gravity coupled to particles, addressing gauge fixing, boundary terms, and determinant cancellations.

Findings

Derived the relation between conjugate momenta and meromorphic quadratic differentials.

Worked out the boundary term for non-compact open universe topology.

Identified cancellation of functional determinants related to string theory punctures.

Abstract

The quantum gravity problem of N point particles interacting with the gravitational field in 2+1 dimensions is approached working out the phase-space functional integral. The maximally slicing gauge is adopted for a non compact open universe with the topology of the plane. The conjugate momenta to the gravitational field are related to a class of meromorphic quadratic differentials. The boundary term for the non compact space is worked out in detail. In the extraction of the physical degrees of freedom functional determinants related to the puncture formulation of string theory occur and cancel out in the final reduction. Finally the ordering problem in the definition of the functional integral is discussed.