Semiclassical and quantum description of motion on noncommutative plane

TL;DR

This paper explores the quantum and semiclassical behavior of a particle in a magnetic field on a noncommutative plane, using various quantization methods and coherent states to analyze gauge dependence and classical correspondence.

Contribution

It introduces a comprehensive analysis combining canonical, coherent state, and semiclassical quantizations for a particle on a noncommutative plane, highlighting gauge dependence and state construction.

Findings

Constructed Malkin-Man'ko coherent states for the system

Analyzed gauge dependence in the quantum theory

Performed numerical semiclassical analysis using specialized states

Abstract

We study the canonical and the coherent state quantization of a particle moving in a magnetic field on a non-commutative plane. Starting from the so called \theta-modified action, we perform the canonical quantization and analyze the gauge dependence of the obtained quantum theory. We construct the Malkin-Man'ko coherent states of the system in question, and the corresponding quantization. On this base, we study the relation between the coherent states and the "classical" trajectories predicted by the \theta-modified action. In addition, we construct different semiclassical states, making use of special properties of circular squeezed states. With the help of these states, we perform the Berezin-Klauder-Toeplitz quantization and present a numerical exploration of the semiclassical behavior of physical quantities in these states.