Noncommutative Dirac quantization condition using the Seiberg-Witten map

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 $θ$, 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.

12 pages