The Quantization of the Chiral Schwinger Model based on the BFT-BFV formalism

TL;DR

This paper applies an improved BFT-BFV Hamiltonian method to the chiral Schwinger Model, systematically constructing first class constraints and deriving the corresponding first class Lagrangian, thus advancing the quantization approach for this model.

Contribution

It introduces an improved BFT-BFV formalism to systematically quantize the chiral Schwinger Model with regularization ambiguity, deriving the first class constraints and Lagrangian.

Findings

First class constraints are systematically constructed.

Dirac brackets match Poisson brackets of extended variables.

First class Lagrangian is derived in configuration space.

Abstract

We apply newly improved Batalin-Fradkin-Tyutin Hamiltonian method to the chiral Schwinger Model in the case of the regularization ambiguity $a>1$. We show that one can systematically construct the first class constraints by the BFT Hamiltonian method, and also show that the well-known Dirac brackets of the original phase space variables are exactly the Poisson brackets of the corresponding modified fields in the extended phase space. Furthermore, we show that the first class Hamiltonian is simply obtained by replacing the original fields in the canonical Hamiltonian by these modified fields. Performing the momentum integrations, we obtain the corresponding first class Lagrangian in the configuration space.