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Aspects of phase-space noncommutative quantum mechanics. (English) Zbl 1364.81158

Summary: In this work some issues in the context of noncommutative quantum mechanics (NCQM) are addressed. The main focus is on finding whether symmetries present in quantum mechanics still hold in the phase-space noncommutative version. In particular, the issues related with gauge invariance of the electromagnetic field and the weak equivalence principle (WEP) in the context of the gravitational quantum well (GQW) are considered. The question of the Lorentz symmetry and the associated dispersion relation is also examined. Constraints are set on the relevant noncommutative parameters so that gauge invariance and Lorentz invariance holds. In opposition, the WEP is verified to hold in the noncommutative setup, and it is only possible to observe a violation through an anisotropy of the noncommutative parameters.

MSC:

81R60 Noncommutative geometry in quantum theory
81R15 Operator algebra methods applied to problems in quantum theory
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