Aspects of Phase-Space Noncommutative Quantum Mechanics

TL;DR

This paper investigates how fundamental symmetries like gauge invariance, Lorentz invariance, and the weak equivalence principle are affected in phase-space noncommutative quantum mechanics, setting constraints on noncommutative parameters.

Contribution

It analyzes the preservation or violation of key symmetries in NCQM and establishes bounds on noncommutative parameters to maintain gauge and Lorentz invariance.

Findings

Gauge and Lorentz invariance can be preserved with specific parameter constraints.

Weak equivalence principle remains valid in NCQM.

Anisotropy in noncommutative parameters could lead to observable violations.

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.