Generalized BRST transformation for relating Proca and Stukelberg theory

This work explores the relationship between the generating functionals associated with first-class and second-class constrained systems through the application of the finite field-dependent BRST (FFBRST) transformation. We rigorously demonstrate this correspondence by carrying out explicit computations within the framework of two distinct models. In particular, we derive the generating functional corresponding to the Proca theory by systematically transforming the generating functional of the Stueckelberg formulation for a massive spin-1 vector field via the FFBRST approach. This analysis underlines the utility of FFBRST transformations in establishing a formal equivalence between different quantization schemes.