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.

13 pages, PlainTeX. A reference and an equation (Ref.[11] and eq.(4.16)) are added, the text is amended, and some contents are deleted. Errors in some equations ((4.13), (4.14), (4.15) and (4.19)) are corrected

References in corpus (11)

• String Theory and Noncommutative Geometry
• Testing Non-commutative QED, Constructing Non-commutative MHD
• Duality and Non-Commutative Gauge Theory
• S-Duality, Noncritical Open String and Noncommutative Gauge Theory
• Superluminal Noncommutative Photons
• Perturbative Analysis of the Seiberg-Witten Map
• Noncommutative Electrodynamics
• D-brane Dualities as Canonical Transformations
• Noncommuting Electric Fields and Algebraic Consistency in Noncommutative Gauge theories
• Hamiltonian formulation of Noncommutative D3--Brane
• On Duality Rotations in Light-Like Noncommutative Electromagnetism

Cited by in corpus (15)

• Exact Seiberg-Witten Map and Induced Gravity from Noncommutativity
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Effective Lagrangian at Cubic Order in Electromagnetic Fields and Vacuum Birefringence
• Dispersion Relations in Noncommutative Theories
• Noncommutative Einstein-Maxwell pp-waves
• Light Propagation in a Background Field for Time-Space Noncommutativity and Axionic Noncommutative QED
• Self-duality, helicity conservation and normal ordering in nonlinear QED
• On the question of deconfinement in noncommutative Schwinger Model
• Noncommutative Electrodynamics with covariant coordinates
• A Note on Duality Symmetry in Nonlinear Gauge Theories
• Electric-Magnetic Dualities in Non-Abelian and Non-Commutative Gauge Theories
• Issues on 3D Noncommutative Electromagnetic Duality
• Equivalence of partition functions for noncommutative U(1) gauge theory and its dual in phase space
• The Lorentz Group, Noncommutative Space-Time, and Nonlinear Electrodynamics in Majorana-Oppenheimer Formalism
• Electromagnetic waves, gravitational coupling and duality analysis