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Frontiers in Physics

Aharonov-Bohm Phase for an Electric Dipole on a Noncommutative Space

Mamutjan Ababekri, Abduwali Anwar, Mamatabdulla Hekim, Reyima Rashidin

Published Jun 27, 2016• 5 citations
Publisher

Abstract

We study the non-relativistic behavior of a particle with electric dipole moment and interacting with external electromagnetic fields on a noncommutative space(NCS). For a special configuration of the field, we derived the phase of an electric dipole as an application of the AB effect to a system composed of two charges. We find that the quantum phase for electric dipole obtains some correction, and this correction depend on the noncommutative parameter explicitly.

DOI
10.3389/fphy.2016.00022

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We study the non-relativistic behavior of a particle with electric dipole moment and interacting with external electromagnetic fields on a noncommutative space(NCS). For a special configuration of the field, we derived the phase of an electric dipole as an application of the AB effect to a system composed of two charges. We find that the quantum phase for electric dipole obtains some correction, and this correction depend on the noncommutative parameter explicitly.
The dynamics of a spin-(1/2) neutral particle possessing electric- and magnetic-dipole moments interacting with external electric and magnetic fields in noncommutative coordinates is obtained. Noncommutativity of space is interposed in terms of a semiclassical constrained Hamiltonian system. The relation between the quantum phase acquired by a particle interacting with an electromagnetic field and the (semi)classical force acting on the system is examined and generalized to establish a formulation of the quantum phases in noncommutative coordinates. The general formalism is applied to physical systems yielding the Aharonov-Bohm, Aharonov-Casher, He-McKellar-Wilkens and Anandan phases in noncommutative coordinates. Bounds for the noncommutativity parameter θ are derived comparing the deformed phases with the experimental data on the Aharonov-Bohm and Aharonov-Casher phases.
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.
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.
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.