The quantization of the chiral Schwinger model based on the BFT-BFV formalism II

TL;DR

This paper applies an improved BFT-BFV Hamiltonian method to the a=1 chiral Schwinger model, successfully deriving a fully gauge-invariant partition function with novel Wess-Zumino terms, advancing the understanding of quantization in nontrivial gauge theories.

Contribution

It introduces an improved BFT-BFV formalism to quantize the a=1 chiral Schwinger model, resolving measure-related issues and deriving a new gauge-invariant partition function with unique WZ terms.

Findings

Explicit gauge-invariant partition function obtained

Resolved non-trivial delta function and Fourier parameter issues

Introduced new Wess-Zumino terms unrelated to gauge symmetry

Abstract

We apply an improved version of Batalin-Fradkin-Tyutin (BFT) Hamiltonian method to the a=1 chiral Schwinger Model, which is much more nontrivial than the a>1.$ one. Furthermore, through the path integral quantization, we newly resolve the problem of the non-trivial $\delta$ function as well as that of the unwanted Fourier parameter $\xi$ in the measure. As a result, we explicitly obtain the fully gauge invariant partition function, which includes a new type of Wess-Zumino (WZ) term irrelevant to the gauge symmetry as well as usual WZ action.