Double Hodge Theory for a particle on Torus

TL;DR

This paper explores the rich mathematical structure of a particle on a torus, revealing four nilpotent BRST symmetries and their algebra, and introduces finite field dependent BRST transformations relevant to toric geometry.

Contribution

It explicitly constructs four independent nilpotent BRST symmetries for a particle on a torus and demonstrates the system's double Hodge theory properties.

Findings

Identified four independent nilpotent BRST symmetries.

Derived the algebra among the symmetry generators.

Constructed finite field dependent BRST transformations.

Abstract

We investigate all possible nilpotent symmetries for a particle on torus. We explicitly construct four independent nilpotent BRST symmetries for such systems and derive the algebra between the generators of such symmetries. We show that such a system has rich mathematical properties and behaves as double Hodge theory. We further construct the finite field dependent BRST transformation for such systems by integrating the infinitesimal BRST transformation systematically. Such a finite transformation is useful in realizing the various theories with toric geometry.