Aharonov–Bohm effect in noncommutative spaces

Abstract

The Aharonov-Bohm effect on the noncommutative plane is considered. Developing the path integral formulation of quantum mechanics, we find the propagation amplitude for a particle in a noncommutative space. We show that the corresponding shift in the phase of the particle propagator due to the magnetic field of a thin solenoid receives certain gauge invariant corrections because of the noncommutativity. Evaluating the numerical value for this correction, an upper bound for the noncommutativity parameter is obtained.

Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics

“…The expression of the obtained phase includes an additional term dependent on the NC space parameter, θ (measured in units of (length) 2 ). The limit on θ found in the AB effect is of the order of √ θ 10 6 GeV −1 which corresponds to a relatively large scale of 1Å [8]. This same approach was extended to the Aharonov-Casher (AC) [10] effect by Li and Wang [11], and Mirza and Zarei [12], in this effect two coherent beams of neutral particles encircle an infinite charged wire.…”

Probing noncommutativities of phase space by using persistent charged current and its asymmetry

“…It has been shown in Refs. [28][29][30][31][32][33][34][35][36][37][38] that magnetic flux due to the permanent dipole moment can modify the Aharonov-Bohm effect [39] as well as the Aharonov-Casher effect [40]. Furthermore, the magnetic flux can also generate a persistent charged current in a metal ring.…”

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

“…The authors of Zhang [11] have suggested the possibility of testing spatial noncommutativity via cold Rydberg atoms. In Chaichian et al [12], Chaichian et al [13], Falomir et al [14], Li and Dulat [15], Mirza and Zarei [16], Li and Wang [17], Mirza et al [18], Singlton and Vagenas [19], Dulat and Ma [20] and Singleton and Ulbricht [21], the AharonovBohm type phase is studied on a NCS and a NCPS. A lower bound is shown to be 1/ √ θ ≥ 10 −6 GeV for the space noncommutativity parameter in Chaichian et al [12].…”

“…In Chaichian et al [12], Chaichian et al [13], Falomir et al [14], Li and Dulat [15], Mirza and Zarei [16], Li and Wang [17], Mirza et al [18], Singlton and Vagenas [19], Dulat and Ma [20] and Singleton and Ulbricht [21], the AharonovBohm type phase is studied on a NCS and a NCPS. A lower bound is shown to be 1/ √ θ ≥ 10 −6 GeV for the space noncommutativity parameter in Chaichian et al [12]. In Mirza and Zarei [16], Li and Wang [17] and Mirza et al [18,22], the Aharonov-Casher phase on a NCS and a NCPS has been studied for a spin-1/2 and a spin-1 particle.…”