Hamiltonian Approach To 2+1 Dimensional Gravity

TL;DR

This paper demonstrates that the reduced particle dynamics in 2+1 dimensional gravity can be formulated as a Hamiltonian system, providing explicit transformations, boundary term analysis, and quantum solutions.

Contribution

It introduces a Hamiltonian formulation for 2+1D gravity in the maximally slicing gauge and derives the quantum Hamiltonian and Green function for two particles.

Findings

The particle dynamics are of Hamiltonian nature in the chosen gauge.

An explicit diffeomorphism relates different geometric gauges.

The quantum two-particle Hamiltonian and Green function are computed.

Abstract

It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge is of hamiltonian nature. We give the exact diffeomorphism which transforms the expression of the spinning cone geometry in the Deser, Jackiw, 't Hooft gauge to the maximally slicing gauge. It is explicitly shown that the boundary term in the action, written in hamiltonian form gives the Hamiltonian for the reduced particle dynamics. The quantum mechanical translation of the two particle Hamiltonian is given and the Green function computed.