One Particle Hilbertspace of 2+1 dimensional Gravity using Non commuting Coordinates

TL;DR

This paper constructs a one-particle Hilbert space for 2+1 dimensional gravity using non-commuting coordinates and curved momentum space, and discusses the formulation of a Schrödinger equation in this context.

Contribution

It introduces a novel approach to quantum gravity in 2+1 dimensions by representing coordinates as non-commuting operators on a curved momentum space.

Findings

Representation of coordinates as non-commuting Hermitian operators

Construction of a one-particle Hilbert space for 2+1D gravity

Outline of a Schrödinger equation in this framework

Abstract

After a review of multi particle solutions in classical 2+1 dimensional gravity we will construct a one particle Hilbert space. As we will use a curved momentum space, the coordinates $x^\mu$ are represented as non commuting Hermitian operators on this Hilbertspace. Finally we will indicate how to construct a Schrodinger equation.