Noncommutative Dirac quantization condition using the Seiberg-Witten map

TL;DR

This paper examines whether the Dirac quantization condition for magnetic monopoles holds in noncommutative space-time, finding it remains valid up to all orders in the noncommutativity parameter using perturbative methods.

Contribution

It demonstrates that the Dirac quantization condition is preserved in noncommutative space-time through all orders of the Seiberg-Witten map expansion.

Findings

DQC remains unmodified up to second order in noncommutativity parameter

The result extends to all orders for a class of noncommutative electric currents

Noncommutative effects do not alter the fundamental quantization condition

Abstract

We investigate the validity of the Dirac quantization condition (DQC) for magnetic monopoles in noncommutative space-time. We use an approach based on an extension of the method introduced by Wu and Yang; the effects of noncommutativity are analyzed using the Seiberg-Witten map and the corresponding deformed Maxwell's equations are discussed. By means of a perturbation expansion in the noncommutativity parameter $\theta$, we show first that the DQC remains unmodified up to the first and second order. This result is then generalized to all orders in the expansion parameter for a class of noncommutative electric currents induced by the Seiberg-Witten map; these currents reduce to the Dirac delta function in the commutative limit.