Coherent state quantization of a particle in de Sitter space

TL;DR

This paper develops a coherent state quantization method for a relativistic particle in de Sitter space, utilizing the SO_0(1,2) symmetry group and introducing a novel coherent state realization of its principal series representation.

Contribution

It introduces a new coherent state quantization approach for a particle in de Sitter space, specifically realizing the principal series representation of SO_0(1,2).

Findings

Coherent state quantization applied to a relativistic particle in de Sitter space.

New realization of the principal series representation of SO_0(1,2).

Method provides a framework for quantizing systems with hyperbolic geometry.

Abstract

We present a coherent state quantization of the dynamics of a relativistic test particle on a one-sheet hyperboloid embedded in a three-dimensional Minkowski space. The group SO_0(1,2) is considered to be the symmetry group of the system. Our procedure relies on the choice of coherent states of the motion on a circle. The coherent state realization of the principal series representation of SO_0(1,2) seems to be a new result.