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arXiv:0802.1116 · Journal of Physics A Mathematical and Theoretical

The He–McKellar–Wilkens effect for spin one particles in non-commutative quantum mechanics

Sayipjamal Dulat, Kang Li, Jianhua Wang

Published Jan 29, 2008• 7 citations
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Abstract

The He–McKellar–Wilkens (HMW) effect for spin one neutral particles in non-commutative quantum mechanics is studied. By solving the Kemmer-like equations on the non-commutative (NC) space and non-commutative phase space, we obtain the topological He–McKellar–Wilkens phase on the NC space and NC phase space respectively, where the additional terms related to the space–space and momentum–momentum non-commutativity are given explicitly.

DOI
10.1088/1751-8113/41/6/065303

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Communications in Theoretical Physics•Jun 1, 2019•3 citations
The He–McKellar–Wilkens (HMW) effect for spin one neutral particles in non-commutative quantum mechanics is studied. By solving the Kemmer-like equations on the non-commutative (NC) space and non-commutative phase space, we obtain the topological He–McKellar–Wilkens phase on the NC space and NC phase space respectively, where the additional terms related to the space–space and momentum–momentum non-commutativity are given explicitly.
In this paper, we study time-dependent He–McKellar–Wilkens (HMW) phase shift, as well as its extension on noncommutative space. We show that for adiabatic varying external magnetic field, the original HMW effect can receive a time-dependent correction. The adiabatic approximation is valid if frequency of the varying external field is smaller enough than the one by which the spinor particle takes a single round. Noncommutative corrections are studied by using Seiberg–Witten map such that the final results are gauge invariant. We find that there are two kinds of contributions, one is purely adiabatic, and the other one is a constant correction and depends on frequency of the external field.
We introduce a new approach to study the noncommutative effects on the neutral particle with anomalous magnetic or electric dipole moments on the 2+12+12+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)U(1)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 θ\thetaθ and the cross section Ae/mA_{e/m}Ae/m​ of the charged line enclosed by the trajectory of beam particle.