Eliminating the chiral anomaly via symplectic embedding approach

TL;DR

This paper presents a method to eliminate the chiral anomaly in the chiral Schwinger model by embedding it into a gauge-invariant framework using symplectic formalism and Wess-Zumino fields, providing a geometric interpretation.

Contribution

It introduces a novel gauge-invariant embedding approach using symplectic formalism and Wess-Zumino fields to remove the chiral anomaly in the model.

Findings

Successfully eliminates the chiral anomaly in the model.

Provides a geometric interpretation of gauge invariance.

Identifies conditions on chiral parameters for anomaly cancellation.

Abstract

The quantization of the chiral Schwinger model $(\chi QED_{2})$ with one-parameter class Faddeevian regularization is hampered by the chiral anomaly, i.e., the Gauss law commutator exhibits Faddeev's anomaly. To overcome this kind of problem, we propose to eliminate this anomaly by embedding the theory through a new gauge-invariant formalism based on the enlargement of the phase space with the introduction of Wess-Zumino(WZ) fields and the symplectic approach. This process opens up a possibility to formulate different, but dynamically equivalent, gauge invariant versions for the model and also gives a geometrical interpretation to the arbitrariness presents on the BFFT and iterative conversion methods. Further, we observe that the elimination of the chiral anomaly imposes a condition on the chiral parameters present on the original model and on the WZ sector.