BRST symmetries in free particle system on toric geometry

TL;DR

This paper explores the BRST symmetries of a free particle on a torus, analyzing its energy spectrum, symplectic structure, and gauge symmetries related to St"uckelberg fields, ghosts, and anti-ghosts.

Contribution

It introduces a detailed analysis of BRST symmetries in a particle system on toric geometry, including spectral and symplectic structure evaluations.

Findings

Energy spectrum of the system is explicitly evaluated.

Symplectic structures of the second-class system are characterized.

BRST symmetry framework is applied to the toric particle system.

Abstract

We study a free particle system residing on a torus to investigate its Becci-Rouet-Stora-Tyutin symmetries associated with its St\"uckelberg coordinates, ghosts and anti-ghosts. By exploiting zeibein frame on the toric geometry, we evaluate energy spectrum of the system to describe the particle dynamics. We also investigate symplectic structures involved in the second-class system on the torus.