Deformed Chern-Simons Theories

TL;DR

This paper introduces a q-deformed Chern-Simons gauge theory where gauge fields q-commute, maintaining a consistent Hamiltonian structure and gauge symmetry, extending classical theory to a deformed algebraic setting.

Contribution

It presents the first explicit construction of a q-deformed Chern-Simons action with a consistent Hamiltonian framework and gauge symmetry.

Findings

The q-deformed gauge potentials and field strengths q-commute.

The Hamiltonian structure remains consistent under deformation.

Constraints form a closed algebra generating q-deformed gauge transformations.

Abstract

We construct a Chern-Simons action for q-deformed gauge theory which is a simple and straightforward generalization of the usual one. Space-time continues to be an ordinary (commuting) manifold, while the gauge potentials and the field strengths become q-commuting fields. Our approach, which is explicitly carried out for the case of `minimal' deformations, has the advantage of leading naturally to a consistent Hamiltonian structure that has essentially all of the features of the undeformed case. For example, using the new Poisson brackets, the constraints form a closed algebra and generate q-deformed gauge transformations.