Dirac Quantization Condition for Monopole in Noncommutative Space-Time

TL;DR

This paper investigates whether the Dirac Quantization Condition (DQC) persists in noncommutative space-time and finds that, to first order in noncommutativity, it remains unchanged from the classical case.

Contribution

The study demonstrates that the DQC remains invariant in a noncommutative space to first order, suggesting it may be robust against space-time noncommutativity effects.

Findings

DQC remains unchanged to first order in noncommutativity parameter

The result supports the conjecture that DQC is unaffected at higher orders

Noncommutative quantum mechanics preserves the classical DQC condition

Abstract

Since the structure of space-time at very short distances is believed to get modified possibly due to noncommutativity effects and as the Dirac Quantization Condition (DQC), $\mu e = \frac{N}{2}\hbar c$, probes the magnetic field point singularity, a natural question arises whether the same condition will still survive. We show that the DQC on a noncommutative space in a model of dynamical noncommutative quantum mechanics remains the same as in the commutative case to first order in the noncommutativity parameter $\theta$, leading to the conjecture that the condition will not alter in higher orders.