Noncommutative Electrodynamics

TL;DR

This paper develops a Lorentz covariant noncommutative classical electrodynamics framework, solving it perturbatively via the Seiberg-Witten map, and explores its solutions and corrections to classical laws.

Contribution

It provides a polynomial action in the field strength for NC electrodynamics, maintaining causality and Lorentz covariance, with all-order perturbative analysis and solution methods.

Findings

Monochromatic plane waves are solutions to all orders.

Developed an iterative method for solving equations of motion.

Calculated corrections to superposition and Coulomb laws.

Abstract

In this paper we define a causal Lorentz covariant noncommutative (NC) classical Electrodynamics. We obtain an explicit realization of the NC theory by solving perturbatively the Seiberg-Witten map. The action is polynomial in the field strenght $F$, allowing to preserve both causality and Lorentz covariance. The general structure of the Lagrangian is studied, to all orders in the perturbative expansion in the NC parameter $\theta$. We show that monochromatic plane waves are solutions of the equations of motion to all orders. An iterative method has been developed to solve the equations of motion and has been applied to the study of the corrections to the superposition law and to the Coulomb law.