Effective Seiberg-Witten map and quantum phase effects for neutral spinor on noncommutative plane

Abstract

We introduce a new approach to study the noncommutative effects on the neutral particle with anomalous magnetic or electric dipole moments on the $2+1$ noncommutative space time. 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 reinterpreting the Aharonov-Casher and He-McKellar-Wilkens effects as consequences of an effective $U(1)$ gauge symmetry. An effective Seiberg-Witten map for this symmetry is introduced when we study the noncommutative corrections. Because Seiberg-Witten map preserves the symmetry, the noncommutative corrections can be investigated systematically. Our results indicate that the noncommutative corrections on the Aharonov-Casher and He-McKellar-Wilkens phases are strongly depend on the ratio between the noncommutative parameter $\theta$ and the cross section $A_{e/m}$ of the charged line enclosed by the trajectory of beam particle.