Novel Symmetries in Christ-Lee Model

TL;DR

This paper explores the fermionic symmetries of the Christ-Lee model's gauge-fixed Lagrangian, revealing a structure akin to de Rham cohomology and providing a simple model for Hodge theory.

Contribution

It demonstrates the presence of four fermionic symmetries in the Christ-Lee model and connects their algebra to de Rham cohomological operators, illustrating a Hodge theory framework.

Findings

Identification of four fermionic symmetries in the model

Algebra of symmetries mirrors de Rham cohomology

Provides physical realization of cohomological operators

Abstract

We demonstrate that the gauge-fixed Lagrangian of the Christ-Lee model respects four fermionic symmetries, namely; (anti-)BRST symmetries, (anti-)co-BRST symmetries within the framework of BRST formalism. The appropriate anticommutators amongst the fermionic symmetries lead to a unique bosonic symmetry. It turns out that the algebra obeyed by the symmetry transformations (and their corresponding conserved charges) is reminiscent of the algebra satisfied by the de Rham cohomological operators of differential geometry. We also provide the physical realizations of the cohomological operators in terms of the symmetry properties. Thus, the present model provides a simple model for the Hodge theory.