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.

16 pages, no figures

References in corpus (6)

• Test of the Equivalence Principle Using a Rotating Torsion Balance
• Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
• Searching for New Physics with Ultrahigh Energy Cosmic Rays
• Berry Phase in the Gravitational Quantum Well and the Seiberg-Witten map
• Entropic Gravity, Phase-Space Noncommutativity and the Equivalence Principle
• Non-Canonical Phase-Space Noncommutativity and the Kantowski-Sachs singularity for Black Holes

Cited by in corpus (31)

• A comparative review of four formulations of noncommutative quantum mechanics
• Generalised uncertainty relations from superpositions of geometries
• Energy-dependent noncommutative quantum mechanics
• Weak equivalence principle in noncommutative phase space and the parameters of noncommutativity
• Parameters of noncommutativity in Lie-algebraic noncommutative space
• Exact solution of two dimensional Dunkl harmonic oscillator in Non-Commutative phase-space
• The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios
• Time-dependent Aharonov-Bohm effect on the noncommutative space
• Significantly super-Chandrasekhar mass-limit of white dwarfs in noncommutative geometry
• Upper bound on the momentum scale in noncommutative phase space of canonical type
• Kinematic variables in noncommutative phase space and parameters of noncommutativity
• Non-Hermitian noncommutative quantum mechanics
• Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics
• Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle
• Probing the noncommutative effects of phase space in the time-dependent Aharonov-Bohm effect
• Macroscopic body in Snyder space and minimal length estimation
• Probing Noncommutativities of Phase Space by Using Persistent Charged Current and Its Asymmetry
• On the Plethora of Representations Arising in Noncommutative Quantum Mechanics and An Explicit Construction of Noncommutative 4-tori
• Constrains of Charge-to-Mass Ratios on Noncommutative Phase Space
• Quantum cloning and teleportation fidelity in the noncommutative phase-space
• Influence of noncommutativity on the motion of Sun-Earth-Moon system and the weak equivalence principle
• Minimal length estimation on the basis of studies of the Sun-Earth-Moon system in deformed space
• Noncommutative momentum and torsional regularization
• Lorentz violation parameters and noncommutative scale
• Relativistic dispersion relation and putative metric structure in noncommutative phase-space
• Comments on noncommutative quantum mechanical systems associated with Lie algebras
• Quantum information aspects of noncommutative quantum mechanics
• Galilei Group with multiple central extension, vorticity and entropy generation: "Exotic" fluid in 3+1-dimensions
• A Phase-Space Noncommutative Picture of Nuclear Matter
• Features of description of composite system's motion in twist-deformed space-time
• Noncommutative Simple Harmonic Oscillator in Quantum Gravitational Well