Abelian 2-Form Gauge Theory: Basic Canonical Brackets and Nilpotency Property of Noether (Anti-)BRST Charges

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we invoke the beauty of the basic canonical (anti)commutators to prove the nilpotency property of the Noether (anti-)BRST charges for the D-dimensional BRST-quantized version of the free Abelian 2-form gauge theory which is endowed with a non-trivial Curci-Ferrari (CF) type restriction. In this proof, we use only the theoretical strength of the Gauss divergence theorem. We demonstrate that, under the off-shell nilpotent (anti-)BRST symmetry transformations, the Noether conserved (anti-)BRST charges are not invariant and they are also found to be not off-shell nilpotent (if we exploit the standard relationship between the continuous symmetry transformations and their generators as the Noether conserved charges). However, these charges become (anti-)BRST invariant and nilpotent if we use (i) the appropriate equations of motion at suitable places, and (ii) the Gauss divergence theorem. We derive the consistently modified versions of the Noether (anti-)BRST charges which are invariant under the off-shell nilpotent (anti-)BRST transformations. We prove the (anti-)BRST invariance of these modified versions of charges by using the basic canonical (anti)commutators, too. We discuss the physicality criteria w.r.t. (i) the conserved Noether (anti-)BRST charges, and (ii) the modified (anti-)BRST invariant versions of the Noether (anti-)BRST charges. We prove the superiority of the latter over the former (in view of the consistency with the Dirac quantization conditions for the gauge theories).