On the Poincar\'e and Gauge symmetry of a model where vector and axial vector interaction get mixed up with different weight

TL;DR

This paper analyzes a (1+1)-dimensional model with mixed vector and axial vector interactions, establishing conditions for physical consistency, gauge invariance, and phase space structure through Dirac's quantization and Wess-Zumino extension.

Contribution

It demonstrates that only a Lorentz covariant masslike term yields a consistent theory and explores gauge symmetry restoration via Wess-Zumino terms and gauge fixing.

Findings

Lorentz covariant masslike term ensures physical consistency.

Gauge invariance can be restored with Wess-Zumino terms.

Gauge fixing is crucial for phase space transmutation.

Abstract

A $(1+1)$ dimensional model where vector and axial vector interaction get mixed up with different weight is considered with a generalized masslike term for gauge field. Through Poincar\'e algebra it has been made confirm that only a Lorentz covariant masslike term leads to a physically sensible theory as long as the number of constraints in the phase space is two. With that admissible masslike term, phase space structure of this model with proper identification of physical canonical pair has been determined using Diracs' scheme of quantization of constrained system. The bosonized version of the model remains gauge non-invariant to start with. Therefore, with the inclusion of appropriate Wess-Zumino term it is made gauge symmetric. An alternative quantization has been carried out over this gauge symmetric version to determine the phase space structure in this situation. To establish that the Wess-Zumino fields allocates themselves in the un-physical sector of the theory an attempts has been made to get back the usual theory from the gauge symmetric theory of the extended phase-space without hampering any physical principle. It has been found that the role of gauge fixing is crucial for this transmutation.