Maxwell's Theory on Non-Commutative Spaces and Quaternions
Abstract
Description
The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quaternion) form. It was shown that the plane electromagnetic wave is the solution of the system of non-linear wave equations of the second order for the electric and magnetic induction fields. We have found the canonical and symmetrical energy-momentum tensors and their non-zero traces. So, the trace anomaly of the energy-momentum tensor was obtained in electrodynamics on non-commutative spaces. It was noted that the dual transformations of electromagnetic fields on non-commutative spaces are broken.
15 pages, LaTeX, typos corrected, submitted to Annales de la Fondation Louis de Broglie
15 pages, LaTeX, typos corrected, submitted to Annales de la Fondation Louis de Broglie