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

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.