Quantum particle on hyperboloid

TL;DR

This paper develops a unique quantization method for a quantum particle constrained to move on a hyperboloid in Minkowski space, leveraging global symmetries and topology for simplified analysis.

Contribution

It introduces a novel quantization approach that accounts for all global symmetries and utilizes topology of canonical variables for particles on hyperboloids.

Findings

Achieved a consistent quantization framework for hyperboloid particles.

Simplified calculations through topology-based canonical variables.

Ensured the quantization respects all global symmetries.

Abstract

We present quantization of particle dynamics on one-sheet hyperboloid embedded in three dimensional Minkowski space. Taking account of all global symmetries enables unique quantization. Making use of topology of canonical variables not only simplifies calculations but also gives proper framework for analysis.