Magnetic Monopole in Noncommutative Space-Time and Wu-Yang Singularity-Free Gauge Transformations

TL;DR

This paper examines whether the Dirac Quantization Condition for magnetic monopoles holds in noncommutative space-time, finding it remains valid up to first order in the noncommutativity parameter using a Wu-Yang inspired approach.

Contribution

It extends the Wu-Yang method to noncommutative gauge theories and shows the DQC is unaffected by noncommutativity at first order.

Findings

DQC remains unmodified up to first order in noncommutativity

Uses perturbation expansion in the noncommutativity parameter

Applicable to a class of noncommutative source terms

Abstract

We investigate the validity of the Dirac Quantization Condition (DQC) for magnetic monopoles in noncommutative space-time. We use an approach which is based on an extension of the method introduced by Wu and Yang. To study the effects of noncommutativity of space-time, we consider the gauge transformations of $U_\star(1)$ gauge fields and use the corresponding deformed Maxwell's equations. Using a perturbation expansion in the noncommutativity parameter $\theta$, we show that the DQC remains unmodified up to the first order in the expansion parameter. The result is obtained for a class of noncommutative source terms, which reduce to the Dirac delta function in the commutative limit.