A Mapping of Different Gauges of Thirring Model Using Generalized BRST Transformation

In this work, we investigate the BRST symmetry structure of the Thirring model in arbitrary dimensions. Starting from the original Thirring Lagrangian, we reformulate it in terms of an auxiliary vector field and subsequently construct a gauge-invariant extension by introducing the Stueckelberg field. The resulting theory admits a local U(1) gauge symmetry, enabling covariant quantization through the inclusion of appropriate gauge-fixing and Faddeev–Popov ghost terms. We demonstrate explicit BRST invariance of the effective action in both axial and Lorentz gauges. Extending the formalism, we derive generalized (finite field-dependent) BRST transformations and analyze their impact on the path integral measure. The associated non-trivial Jacobian is computed explicitly, and we show that it modifies only the BRST-exact sector of the action, thereby preserving the physical content of the theory. As an application, we establish a precise mapping between generating functionals in axial and Lorentz gauges, mediated through the generalized BRST symmetry. This construction highlights the equivalence of different gauge-fixed versions of the Thirring model and provides a unified framework for studying its BRST cohomological structure.