Deformed Chern-Simons theories

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.