Batalin-Tyutin Quantization of the Chiral Schwinger Model

TL;DR

This paper applies the Batalin-Tyutin formalism to quantize the chiral Schwinger Model, systematically constructing gauge-invariant Hamiltonians and revealing new Wess-Zumino terms for specific parameters.

Contribution

It introduces a systematic method for quantizing the chiral Schwinger Model using Batalin-Tyutin formalism, including novel Wess-Zumino terms at a special parameter value.

Findings

Constructed first class constraints and Hamiltonian for the model.

Derived gauge-invariant Lagrangian with Wess-Zumino terms for different parameters.

Discovered new Wess-Zumino terms irrelevant to gauge symmetry at a specific parameter value.

Abstract

We quantize the chiral Schwinger Model by using the Batalin-Tyutin formalism. We show that one can systematically construct the first class constraints and the desired involutive Hamiltonian, which naturally generates all secondary constraints. For $a>1$, this Hamiltonian gives the gauge invariant Lagrangian including the well-known Wess-Zumino terms, while for $a=1$ the corresponding Lagrangian has the additional new type of the Wess-Zumino terms, which are irrelevant to the gauge symmetry.