Constraints and conserved charges for modified massive and massless Abelian 1-form and 2-form theories: a brief review

We demonstrate that the generators for the local, continuous and infinitesimal classical gauge symmetry transformations in the cases of (1) the Stückelberg-modified massive Abelian 1-form and 2-form theories, and (2) the massless Abelian 1-form and 2-form free theories owe their origin to the first-class constraints (on these theories). We discuss the appearance of these constraints at the quantum level, within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, through the physicality criteria w.r.t. the conserved and nilpotent (anti-)BRST charges. One of the highlights of our present investigation is the derivation of the nilpotent versions of the (anti-)BRST charges (from the standard non-nilpotent Noether (anti-)BRST charges) which lead to the appearance of the operator forms of the first-class constraints through the physicality criteria at the quantum level in the context of the modified massive and massless Abelian 2-form theories. We also comment on (1) the existence of the Curci-Ferrari (CF) type restrictions on the Abelian 2-form theories ( with and without mass), (2) the modifications in the Stückelberg-technique for the massive 2D Abelian 1-form and 4D Abelian 2-form theories and their consequences, and (3) the off-shell nilpotent version of the conserved co-BRST charge and its role in the physicality criteria for the Stückelberg-modified 4D massive Abelian 2-form theory.