Gauge Covariance of the Aharonov-Bohm Phase in Noncommutative Quantum Mechanics

Details Gauge Covariance of the Aharonov-Bohm Phase in Noncommutative Quantum Mechanics Gauge Covariance of the Aharonov-Bohm Phase in Noncommutative Quantum Mechanics

2008-04-22

arxiv.org/abs/0804.3565v3

Phys.Lett.B666:199-204,2008

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, 1 figure, references added, some points clarified further, minor corrections

Scientific paper

10.1016/j.physletb.2008.06.050

The gauge covariance of the wave function phase factor in noncommutative quantum mechanics (NCQM) is discussed. We show that the naive path integral formulation and an approach where one shifts the coordinates of NCQM in the presence of a background vector potential leads to the gauge non-covariance of the phase factor. Due to this fact, the Aharonov-Bohm phase in NCQM which is evaluated through the path-integral or by shifting the coordinates is neither gauge invariant nor gauge covariant. We show that the gauge covariant Aharonov-Bohm effect should be described by using the noncommutative Wilson lines, what is consistent with the noncommutative Schr\"odinger equation. This approach can ultimately be used for deriving an analogue of the Dirac quantization condition for the magnetic monopole.

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