Canonical Quantization of Gravitating Point Particles in 2+1 Dimensions

TL;DR

This paper presents a formalism for quantizing gravitating point particles in 2+1 dimensions, revealing that the quantum model inherently discretizes both time and spacelike distances in a unique manner.

Contribution

It introduces a novel quantization approach that naturally leads to discretized time and spacelike distances in a 2+1 dimensional gravity model.

Findings

Quantum model automatically discretizes time.

Spacelike distances are discretized in a special way.

First model with inherent time discretization in quantum gravity.

Abstract

A formalism previously introduced by the author using tesselated Cauchy surfaces is applied to define a quantized version of gravitating point particles in 2+1 dimensions. We observe that this is the first model whose quantum version automatically discretizes time. But also spacelike distances are discretized in a very special way.