BATALIN-FRADKIN-TYUTIN EMBEDDING OF A SELF-DUAL MODEL AND THE MAXWELL-CHERN-SIMONS THEORY

TL;DR

This paper embeds the self-dual model into a gauge-invariant framework using the Batalin-Fradkin-Tyutin formalism, linking it to the Maxwell-Chern-Simons theory and clarifying the role of gauge fields.

Contribution

It demonstrates the conversion of the self-dual model into a first-class system and identifies gauge-invariant fields with observables and fundamental fields, providing a unified phase-space formulation.

Findings

Embedded the self-dual model into a gauge-invariant system.

Identified gauge-invariant fields with Maxwell-Chern-Simons observables.

Constructed the phase-space partition function for the embedded model.

Abstract

We convert the self-dual model of Townsend, Pilch, and Nieuwenhuizen to a first-class system using the generalized canonical formalism of Batalin, Fradkin, and Tyutin and show that gauge-invariant fields in the embedded model can be identified with observables in the Maxwell-Chern-Simons theory as well as with the fundamental fields of the self-dual model. We construct the phase-space partition function of the embedded model and demonstrate how a basic set of gauge-variant fields can play the role of either the vector potentials in the Maxwell-Chern-Simons theory or the fundamental fields of the self-dual model by appropriate choices of gauge.