Dual BRST symmetry for QED

TL;DR

This paper introduces a dual BRST symmetry in 2D Abelian gauge theory, revealing a new invariance related to gauge-fixing and connecting the algebra of symmetries to de Rham cohomology, thus modeling Hodge theory.

Contribution

It demonstrates the existence of a co(dual)-BRST symmetry in 2D QED, linking gauge invariance, chiral transformations, and Hodge theory within a unified framework.

Findings

Dual BRST symmetry exists in 2D QED.

The symmetry relates to gauge-fixing invariance.

The algebra of symmetries mirrors de Rham cohomology.

Abstract

We show the existence of a co(dual)-BRST symmetry for the usual BRST invariant Lagrangian density of an Abelian gauge theory in two dimensions of space-time where a U(1) gauge field is coupled to the Noether conserved current (constructed by the Dirac fields). Under this new symmetry, it is the gauge-fixing term that remains invariant and the symmetry transformations on the Dirac fields are analogous to the chiral transformations. This interacting theory is shown to provide a tractable field theoretical model for the Hodge theory. The Hodge dual operation is shown to correspond to a discrete symmetry in the theory and the extended BRST algebra for the generators of the underlying symmetries turns out to be reminiscent of the algebra obeyed by the de Rham cohomology operators of differential geometry.