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Communications in Theoretical Physics

Time-dependent Aharonov–Casher effect on noncommutative space

Tao Wang, Kai Ma

Published Nov 10, 2022• 5 citations
Publisher

Abstract

Abstract In this paper, we study the time-dependent Aharonov–Casher effect and its corrections due to spatial noncommutativity. Given that the charge of the infinite line in the Aharonov–Casher effect can adiabatically vary with time, we show that the original Aharonov–Casher phase receives an adiabatic correction, which is characterized by the time-dependent charge density. Based on Seiberg–Witten map, we show that noncommutative corrections to the time-dependent Aharonov–Casher phase contains not only an adiabatic term but also a constant contribution depending on the frequency of the varying electric field.

DOI
10.1088/1572-9494/aca1ac

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Abstract In this paper, we study the time-dependent Aharonov–Casher effect and its corrections due to spatial noncommutativity. Given that the charge of the infinite line in the Aharonov–Casher effect can adiabatically vary with time, we show that the original Aharonov–Casher phase receives an adiabatic correction, which is characterized by the time-dependent charge density. Based on Seiberg–Witten map, we show that noncommutative corrections to the time-dependent Aharonov–Casher phase contains not only an adiabatic term but also a constant contribution depending on the frequency of the varying electric field.
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 study the time-dependent Aharonov–Bohm effect on the noncommutative space. Because there is no net Aharonov–Bohm phase shift in the time-dependent case on the commutative space, therefore, a tiny deviation from zero indicates new physics . Based on the Seiberg–Witten map we obtain the gauge invariant and Lorentz covariant Aharonov–Bohm phase shift in general case on noncommutative space. We find there are two kinds of contribution: momentum-dependent and momentum-independent corrections. For the momentum-dependent correction, there is a cancellation between the magnetic and electric phase shifts, just like the case on the commutative space. However, there is a non-trivial contribution in the momentum-independent correction. This is true for both the time-independent and time-dependent Aharonov–Bohm effects on the noncommutative space. However, for the time-dependent Aharonov–Bohm effect, there is no overwhelming background which exists in the time-independent Aharonov–Bohm effect on both commutative and noncommutative space. Therefore, the time-dependent Aharonov–Bohm can be sensitive to the spatial noncommutativity. The net correction is proportional to the product of the magnetic fluxes through the fundamental area represented by the noncommutative parameter θ , and through the surface enclosed by the trajectory of charged particle. More interestingly, there is an anti-collinear relation between the logarithms of the magnetic field B and the averaged flux Φ / N ( N is the number of fringes shifted). This nontrivial relation can also provide a way to test the spatial noncommutativity. For B Φ / N ∼ 1 , our estimation on the experimental sensitivity shows that it can reach the 10 GeV scale. This sensitivity can be enhanced by using stronger magnetic field strength , larger magnetic flux, as well as higher experimental precision on the phase shift.
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.
By identifying the model of a relativistic spin-half neutral particle which possesses magnetic and electric dipole moments interacting with an electromagnetic field as the [Formula: see text] gauge theory, we study the Anandan phase in [Formula: see text]-dimensional noncommutative space–time by applying the Seiberg–Witten map. We find that up to the first order of the noncommutative parameter, Anandan phase does not receive any corrections due to the spatial noncommutativity. Our result also indicates that phases of either Aharonov–Casher or He–Mckellar–Wilkens effects can receive corrections due to spatial noncommutativity.
In this paper we give a covariant expression for Aharonov–Casher phase. This expression is a combination of the canonical electric field, Aharonov–Casher phase plus a magnetic field phase shift. We use this covariant expression for the Aharonov–Casher phase to investigate the case of a neutral particle with a non-zero magnetic moment moving in the time dependent electric and magnetic fields of a plane electromagnetic wave background. We focus on the case where the magnetic moment of the particle is oriented so that both the electric and magnetic fields lead to non-zero phases, and we look at the interplay between these electric and magnetic phases.