Testing spatial noncommutativity via the Aharonov-Bohm effect

Abstract

The possibility of detecting noncommutative space relics is analyzed using the Aharonov-Bohm effect. We show that, if space is noncommutative, the holonomy receives non-trivial kinematical corrections that will produce a diffraction pattern even when the magnetic flux is quantized. The scattering problem is also formulated, and the differential cross section is calculated. Our results can be extrapolated to high energy physics and the bound θ ∼ [10 TeV] −2 is found. If this bound holds, then noncommutative effects could be explored in scattering experiments measuring differential cross sections for small angles. The bound state Aharonov-Bohm effect is also discussed.

Aharonov-Bohm effect in a class of noncommutative theories

“…This is completely different than in conventional noncommutative quantum mechanics where the differential cross section [16] may depend on theta in the case of small angle. Therefore, the differential cross section for our problem is the same as in the Aharonov-Bohm effect for spin 1/2 particles.…”

“…which is the standard result for the Aharonov-Bohm effect (see for example [16]). Therefore, the differential cross section, for a beam polarized parallel to the solenoid direction, the cross section turns out to be…”

Field Quantization on Noncommutative Phase Space

“…In literature the NC quantum mechanics and NC quantum field theory have been studied extensively, in literatures many interesting topics of NC quantum theories have been extensively investigated, from the Aharonov-Bohm effect to the quantum Hall effect [1][2][3][4][5][6][7]. Recently quantum theory of NC fields has been proposed as a possible field theory generalization of NC quantum mechanics [8][9][10][11].…”

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].…”