Symplectic gauge invariant reformulation of a free particle system on toric geometry

TL;DR

This paper develops a gauge-invariant reformulation of a free particle constrained on a torus, using symplectic formalism, and establishes its BRST symmetries, contributing to the understanding of constrained quantum systems.

Contribution

It introduces a symplectic gauge invariant approach to quantize a particle on a toric geometry, extending the Faddeev-Jackiw formalism with BRST symmetry analysis.

Findings

Successfully reformulated the system as a gauge theory

Derived off-shell nilpotent BRST symmetries

Quantized the constrained particle system

Abstract

We deduce the constraint structure and subsequently quantize a free particle system residing on a torus satisfying the geometric constraint $(r-a)=0$, within the framework of modified Faddeev-Jackiw formalism. Further, we reformulate the system as a gauge theory by the means of symplectic gauge invariant formalism. Finally, we establish the off-shell nilpotent and absolutely anti-commuting (anti-)BRST symmetries of the reformulated gauge invariant theory.