An Alternative Formulation of Hall Effect and Quantum Phases in Noncommutative Space

TL;DR

This paper presents a new approach to quantum mechanics in noncommutative space, analyzing the Hall effect and quantum phases, resulting in velocity-independent $ heta$-deformed phases.

Contribution

It introduces an alternative formulation of noncommutative quantum mechanics that avoids star products, providing new insights into quantum phases and the Hall effect.

Findings

Velocity-independent $ heta$-deformed phases identified.

New formulation simplifies analysis of noncommutative quantum systems.

Potential implications for quantum Hall effect studies.

Abstract

A recent method of constructing quantum mechanics in noncommutative coordinates, alternative to implying noncommutativity by means of star product is discussed. Within this approach we study Hall effect as well as quantum phases in noncommutative coordinates. The $\theta$--deformed phases which we obtain are velocity independent.