Three Dimensional Gauge Theory with Topological and Non-topological Mass: Hamiltonian and Lagrangian Analysis

TL;DR

This paper analyzes three-dimensional gauge theories with topological and non-topological mass terms, providing a Hamiltonian and Lagrangian solution, and computes the charge current algebra including the Schwinger term.

Contribution

It offers a comprehensive Hamiltonian and Lagrangian analysis of 3D gauge theories with topological and non-topological masses, including bosonization and current algebra calculations.

Findings

Spectrum of modes determined in the MCS Proca theory

Charge current algebra including Schwinger term computed

Bosonization relates gauge fields to fermion currents

Abstract

Three dimensional (abelian) gauged massive Thirring model is bosonized in the large fermion mass limit. A further integration of the gauge field results in a non-local theory. A truncated version of that is the Maxwell Chern Simons (MCS) theory with a conventional mass term or MCS Proca theory. This gauge invariant theory is completely solved in the Hamiltonian and Lagrangian formalism, with the spectra of the modes determined. Since the vector field constituting the model is identified (via bosonization) to the fermion current, the charge current algebra, including the Schwinger term is also computed in the MCS Proca model.