GAUGE TRANSFORMATIONS, BRST COHOMOLOGY AND WIGNER'S LITTLE GROUP

Abstract

We discuss the (dual-)gauge transformations and BRST cohomology for the two (1+1)-dimensional (2D) free Abelian one-form and four (3+1)-dimensional (4D) free Abelian two-form gauge theories by exploiting the (co-)BRST symmetries (and their corresponding generators) for the Lagrangian densities of these theories. For the 4D free two-form gauge theory, we show that the changes on the antisymmetric polarization tensor eμν(k) due to (i) the (dual-)gauge transformations corresponding to the internal symmetry group, and (ii) the translation subgroup T(2) of the Wigner's little group, are connected with each other for the specific relationships among the parameters of these transformation groups. In the language of BRST cohomology defined with respect to the conserved and nilpotent (co-)BRST charges, the (dual-)gauge transformed states turn out to be the sum of the original state and the (co-)BRST exact states. We comment on (i) the quasitopological nature of the 4D free two-form gauge theory from the degrees of freedom count on eμν(k), and (ii) the Wigner's little group and the BRST cohomology for the 2D one-form gauge theory vis-à-vis our analysis for the 4D two-form gauge theory.