Magnetic Monopoles in Noncommutative Space-Time: Second Order of Perturbation

TL;DR

This paper examines the Dirac Quantization Condition for magnetic monopoles in noncommutative space-time, revealing that second order corrections in the noncommutativity parameter cause the DQC to lose its topological nature.

Contribution

It extends previous work by including second order perturbative corrections, showing that the DQC must be modified and is no longer purely topological in noncommutative space-time.

Findings

Second order corrections break the topological invariance of DQC.

DQC depends on space-time points in noncommutative geometry.

The modified DQC includes perturbative corrections.

Abstract

We investigate the validity of the Dirac Quantization Condition (DQC) for magnetic monopoles in noncommutative space-time using an extension of the method used by Wu and Yang. We continue the work started in [1] where it was shown that the DQC can be kept unmodified in the first order of the perturbative expansion in the noncommutativity parameter \theta. Here we include second order corrections and find that, in order to find solutions to the noncommutative Maxwell's equations described by the $U_\star(1)$ group, the DQC needs to be modified by perturbative corrections that introduce a dependence on space-time points. Thus the DQC fails to be a topological property of noncommutative space-time. We comment on the possible origin of this difference.