Duality Symmetry and Plane Waves in Non-Commutative Electrodynamics

Abstract

We generalise the electric-magnetic duality in standard Maxwell theory to its non-commutative version. Both space-space and space-time non-commutativity are necessary. The duality symmetry is then extended to a general class of non-commutative gauge theories that goes beyond non-commutative electrodynamics. As an application of this symmetry, plane wave solutions are analysed. Dispersion relations following from these solutions show that general non-commutative gauge theories other than electrodynamics admits two waves with distinct polarisations propagating at different velocities in the same direction.