Generalized BRST Symmetry and the BV Approach to Constrained Gauge Theories

We present a comprehensive investigation of BRST invariance, and the structure of constraints. Starting from the Proca model, which describes a massive spin-1 vector field characterized by second-class constraints and the absence of gauge symmetry, we construct its gauge-invariant extension via the Stueckelberg mechanism. This procedure promotes the system to a first-class theory, thereby enabling a consistent BRST quantization. Within the BV formalism, we formulate BRST symmetry as a canonical transformation generated by the antibracket with the extended quantum action and systematically develop its generalized (finite field-dependent) extension. We demonstrate that while such generalized BRST transformations leave the action invariant, they induce a nontrivial Jacobian in the functional measure, contributing only BRST-exact terms and thus preserving the physical content of the theory. We further construct the extended BV action for the Stueckelberg theory and verify that it satisfies both the classical and quantum master equations. Gauge fixing is implemented through an appropriate fermionic functional, leading to a consistent gauge-fixed action via elimination of antifields. By explicitly integrating out the auxiliary and ghost degrees of freedom, we show that the Proca theory naturally emerges as a reduced form of the Stueckelberg theory. In the BV framework, this correspondence is interpreted as a mapping between distinct solutions of the quantum master equation, thereby establishing the equivalence of the two formulations at the level of physical observables.