ABSOLUTE ANTICOMMUTATIVITY OF THE NILPOTENT SYMMETRIES IN THE HAMILTONIAN FORMALISM: FREE ABELIAN 2-FORM GAUGE THEORY

Abstract

The celebrated Curci–Ferrari (CF) type of restrictions are invoked to obtain the off-shell nilpotent and absolutely anticommuting (anti-)BRST as well as (anti-)co-BRST symmetry transformations in the context of the Lagrangian description of the physical four (3+1)-dimensional (4D) free Abelian 2-form gauge theory. We show that the above CF-type conditions, which turn out to be the secondary constraints of the theory, remain invariant with respect to the time-evolution of the above 2-form gauge system in the Hamiltonian formulation. This time-evolution invariance (i) physically ensures the linear independence of the BRST versus anti-BRST as well as co-BRST versus anti-co-BRST symmetry transformations, and (ii) provides a logical reason behind the imposition of the above CF-type restrictions in the proof of the absolute anticommutativity of the off-shell nilpotent (anti-)BRST as well as (anti-)co-BRST symmetry transformations.