Classical electrodynamics in a space with spin noncommutativity of coordinates

Abstract

We propose a new relativistic Lorentz-invariant spin-noncommutative algebra. Using the Weyl ordering of noncommutative position operators, we build an analogue of the Moyal-Groenewald product for the proposed algebra. The Lagrange function of an electromagnetic field in the space with spin noncommutativity is constructed. In such a space electromagnetic field becomes non-abelian. A gauge transformation law of this field is also obtained. Exact nonlinear field equations of noncommutative electromagnetic field are derived from the least action principle. Within the perturbative approach we consider field of a point charge in a constant magnetic field and interaction of two plane waves. An exact solution of a plane wave propagation in a constant magnetic and electric fields is found.

15 pages

References in corpus (6)

• Noncommutative Point Sources
• Lagrangian formulation for Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations
• Magnetic-Dipole Spin Effects in Noncommutative Quantum Mechanics
• Noncommutativity due to spin
• Hydrogen atom in rotationally invariant noncommutative space
• Perturbation of the ns energy levels of the hydrogen atom in rotationally invariant noncommutative space

Cited by in corpus (6)

• Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity
• Noncommutative Spaces and Poincaré Symmetry
• Time-dependent Aharonov-Bohm effect on the noncommutative space
• Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle
• Chiral Spin Noncommutative Space and Anomalous Dipole Moments
• Vacuum Pair Creation in Spin Noncommutative of Coordinates: Volkov Background and Constant Electric Field