Wigner’s Little Group and Brst Cohomology for One-form Abelian Gauge Theory

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.