Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics

Abstract

Quantum mechanics in noncommutative space modifies the standard result of the Aharonov-Bohm effect for electrons and other recent quantum effects. Here we obtain the phase in noncommutative space for the Spavieri effect, a generalization of Aharonov-bohm effect which involving a coherent superposition of particles with opposite charges moving along single open interferometric path. By means of the experimental considerations a limit √ θ ≃ (0, 13T eV) −1 is achieved, improving by 10 orders of magnitude the derived by Chaichian et. al. for the Aharonov-Bohm effect. It is also shown that the noncommutative phases of the Aharonov-Casher and He-McKellar-Willkens effects are nullified in the current experimental tests.

Klein-Gordon Theory in Noncommutative Phase Space

“…For ∂ t x i = 0, using the parameterization scheme (20) and plugging the gauge potential (26) into (34), the gauge field is obtained…”

“…[21][22][23] The noncommutative phase space also extended to the smear Hilbert space to generalize the uncertainty relations. These generalized quantization schemes turn out some novel ef-fects coming from the noncommutative phase space, such as Aharonov-Bohm effect [24][25][26],…”

Time-dependent Aharonov–Casher effect on noncommutative space

“…Electromagnetic interactions of dipole moments can receive additional contributions [21][22][23][24][25][26][27][28], and degenerate levels of hydrogen energy spectrum can be removed [29][30][31]. Apart from the dynamical effects, topological properties of the ordinary electromagnetic theory can also be distorted, for instance, the Aharonov-Bohm (AB) effect [32] and the Aharonov-Casher (AC) effect [33] on noncommutative spacetime [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] as well as in the spacetime of topological defects [49][50][51], can receive non-trivial corrections. Both AB and AC phases are purely quantum effects, and are closely related to gauge symmetry of the electromagnetic interactions.…”

Chiral Spin Noncommutative Space and Anomalous Dipole Moments

“…For instance, distortions of energy levels of atoms [15][16][17][18][19][20], contributions to the topological phase effects [11,12,[21][22][23][24][25][26], corrections on the spin-orbital interactions [27][28][29][30][31][32], as well as deformations of quantum speeds of relativistic charged particles [33][34][35][36].…”