New local symmetry for QED in two dimensions

TL;DR

This paper introduces a new local, covariant, nilpotent symmetry in two-dimensional QED that extends the BRST algebra and relates to de Rham cohomology, offering insights into gauge fixing and chiral transformations.

Contribution

It discovers a novel symmetry in 2D QED that extends the BRST algebra and connects gauge fixing with Hodge theory, providing new theoretical insights.

Findings

Identifies a new local, covariant, nilpotent symmetry in 2D QED.

Derives an extended BRST algebra analogous to de Rham cohomology.

Discusses implications for BRST cohomology and Hodge decomposition.

Abstract

A new local, covariant and nilpotent symmetry is shown to exist for the interacting BRST invariant U(1) gauge theory in two dimensions of space-time. Under this new symmetry, it is the gauge-fixing term that remains invariant and the corresponding transformations on the Dirac fields turn out to be the analogue of chiral transformations. The extended BRST algebra is derived for the generators of all the underlying symmetries, present in the theory. This algebra turns out to be the analogue of the algebra obeyed by the de Rham cohomology operators of differential geometry. Possible interpretations and implications of this symmetry are pointed out in the context of BRST cohomology and Hodge decomposition theorem.