Free Abelian 2-form gauge theory: BRST approach

We discuss various symmetry properties of the Lagrangian density of a four- (3+1)-dimensional (4D) free Abelian 2-form gauge theory within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism. The present free Abelian gauge theory is endowed with a Curci–Ferrari type condition, which happens to be a key signature of the 4D non-Abelian 1-form gauge theory. In fact, it is due to the above condition that the nilpotent BRST and anti-BRST symmetries of our present theory are found to be absolutely anticommuting in nature. For the present 2-form theory, we discuss the BRST, anti-BRST, ghost and discrete symmetry properties of the Lagrangian densities and derive the corresponding conserved charges. The algebraic structure, obeyed by the above conserved charges, is deduced and the constraint analysis is performed with the help of physicality criteria, where the conserved and nilpotent (anti-) BRST charges play completely independent roles. These physicality conditions lead to the derivation of the above Curci–Ferrari type restriction, within the framework of the BRST formalism, from the constraint analysis.