Wigner's little group and BRST cohomology for one-form Abelian gauge theory

TL;DR

This paper explores the connection between gauge transformations, dual-gauge transformations, and Wigner's little group in the context of 4D Abelian gauge theory, revealing new insights through BRST cohomology and Hodge decomposition.

Contribution

It establishes a novel link between dual-gauge transformations and Wigner's little group, extending the understanding of gauge symmetries in quantum field theory.

Findings

Dual-gauge transformations are connected to the translation subgroup T(2) of Wigner's little group.

The relationship between dual-gauge transformations and the little group is a new observation.

BRST cohomology and Hodge decomposition are used to analyze these symmetries.

Abstract

We discuss the (dual-)gauge transformations for the gauge-fixed Lagrangian density and establish their intimate connection with the translation subgroup T(2) of the Wigner's little group for the free one-form Abelian gauge theory in four $(3 + 1)$-dimensions (4D) of spacetime. Though the relationship between the usual gauge transformation for the Abelian massless gauge field and T(2) subgroup of the little group is quite well-known, such a connection between the dual-gauge transformation and the little group is a new observation. The above connections are further elaborated and demonstrated in the framework of Becchi-Rouet-Stora-Tyutin (BRST) cohomology defined in the quantum Hilbert space of states where the Hodge decomposition theorem (HDT) plays a very decisive role.