Duality Symmetry and Plane Waves in Non-Commutative Electrodynamics

TL;DR

This paper extends electric-magnetic duality to non-commutative gauge theories, analyzing plane wave solutions and revealing that such theories can support two distinct waves with different velocities.

Contribution

It generalizes duality symmetry to non-commutative gauge theories beyond electrodynamics and studies their plane wave solutions.

Findings

Duality symmetry is extended to non-commutative gauge theories.

Plane wave solutions exhibit two waves with different velocities.

Dispersion relations differ from classical 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.