Topologically Massive Non-Abelian Gauge Theories: Constraints and Deformations

TL;DR

This paper analyzes three non-Abelian topologically massive gauge theories within the canonical framework, focusing on their constraints, deformations, and the role of auxiliary fields, clarifying their relationships and differences.

Contribution

It provides a Hamiltonian formulation of the naive non-Abelian model and explores how the other two models are obtained by deforming its constraints, highlighting their distinct features.

Findings

The dynamical 2-form theory cannot be viewed as an embedded version of the naive non-Abelian model.

The role of the auxiliary vector field in the dynamical 2-form theory is clarified.

The gauge algebra and reducibility aspects of the models are discussed.

Abstract

We study the relationship between three non-Abelian topologically massive gauge theories, viz. the naive non-Abelian generalization of the Abelian model, Freedman-Townsend model and the dynamical 2-form theory, in the canonical framework. Hamiltonian formulation of the naive non-Abelian theory is presented first. The other two non-Abelian models are obtained by deforming the constraints of this model. We study the role of the auxiliary vector field in the dynamical 2-form theory in the canonical framework and show that the dynamical 2-form theory cannot be considered as the embedded version of naive non-Abelian model. The reducibility aspect and gauge algebra of the latter models are also discussed.