Seiberg-Witten map and quantum phase effects for neutral Dirac particle on noncommutatiave plane

TL;DR

This paper introduces a new method using the Seiberg-Witten map to analyze noncommutative effects on neutral Dirac particles, revealing velocity-dependent and independent phase corrections in quantum interference phenomena.

Contribution

It presents a novel approach employing the Seiberg-Witten map to study noncommutative corrections in quantum phases, ensuring gauge symmetry preservation and identifying new velocity-independent effects.

Findings

Noncommutative corrections include velocity-dependent and independent terms.

The velocity-independent term is a new contribution not previously identified.

Experimental sensitivity can be enhanced by reducing the charge line cross section.

Abstract

We provide a new approach to study the noncommutative effects on the neutral Dirac particle with anomalous magnetic or electric dipole moment on the noncommutative plane. The advantages of this approach are demonstrated by investigating the noncommutative corrections on the Aharonov-Casher and He-McKellar-Wilkens effects. This approach is based on the effective $U(1)$ gauge symmetry for the electrodynamics of spin on the two dimensional space. The Seiberg-Witten map for this symmetry is then employed when we study the noncommutative corrections. Because the Seiberg-Witten map preserves the gauge symmetry, the noncommutative corrections can be defined consistently with the ordinary phases. Based on this approach we find the noncommutative corrections on the Aharonov-Casher and He-McKellar-Wilkens phases consist of two terms. The first one depends on the beam particle velocity and consistence with the previous results. However the second term is velocity-independent and then completely new. Therefore our results indicate it is possible to investigate the noncommutative space by using ultra-cold neutron interferometer in which the velocity-dependent term is negligible. Furthermore, both these two terms are proportional to the ratio between the noncommutative parameter $\theta$ and the cross section $A_{e/m}$ of the electrical/magnetic charged line enclosed by the trajectory of beam particles. Therefore the experimental sensitivity can be significantly enhanced by reduce the cross section of the charge line $A_{e/m}$.