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We demonstrate the existence of the first-class constraints on the masslessAbelian 3-form theory which generate the classical gauge symmetrytransformations for this theory in any arbitrary D-dimension of spacetime. Wewrite down the explicit expression for the generator in terms of thesefirst-class constraints. Using the celebrated Noether theorem, corresponding tothe gauge symmetry transformations, we derive the Noether conserved current andconserved charge. The latter is connected with the first-class constraints ofthe theory in a subtle manner as we demonstrate clearly in our presentinvestigation. We comment on the first-class constraints within the frameworkof Becchi-Rouet-Stora-Tyutin (BRST) formalism where the conserved (anti-)BRSTcharges are the generalizations of the above generator for the classical gaugesymmetry transformation. The standard Noether conserved (anti-)BRST charges arefound to be non-nilpotent. We derive the nilpotent versions of the (anti-)BRSTcharges. One of the interesting observations of our present endeavor is theresult that only the nilpotent versions of the conserved (anti-)BRST chargeslead to the annihilation of the physical states by the operator form of thefirst-class constraints at the quantum level which is consistent with the Diracquantization condition for the systems that are endowed with any kind ofconstraints. We comment on the existence of the Curci-Ferrari (CF) typerestrictions from different theoretical angles, too.

Constraints, Symmetry Transformations and Conserved Charges for Massless Abelian 3-Form Theory