Aspects of phase-space noncommutative quantum mechanics

Abstract

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 set up, and it is only possible to observe a violation through an anisotropy of the noncommutative parameters.

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

“…However, in consideration that the momentum operators are defined as the derivatives with respect to coordinates, it is natural to consider a further extension with noncommutative momentum operators defined by the algebra (we will use the notation P μ to denote the momentum vectors in this space) [35,41,[45][46][47][48][49][50][51],…”

“…Physical effects of the above extension have been studied in various aspects [35,41,[45][46][47][48][49][50][51]. And recently, a more general extension on the generators of the whole Poincaré group was conducted in Ref.…”

“…While the coordinate noncommutativity cannot be taken into account by using a simple shift method, the representation in Eq. (3) in terms of ordinary coordinate and momentum operators can realize the algebra in (2) [45],…”

“…However, the analysis in Ref. [41] was done by using a simple shift method that in general cannot lead to a gauge-invariant result [31,32,38,45]. Furthermore, the persistent current in the real metal ring is also affected by temperature, cross section, etc.…”

Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics

“…Recently there has been a growing interest in studying quantum mechanics in noncommutative (NC) space [1][2][3] [4][5] [6]. Because quantum nature experiments are measured with high precision, these are feasible scenarios for setting limits on the experimental manifestation of NC space.…”