Coherent states of a particle in magnetic field and Stieltjes moment problem

TL;DR

This paper presents a solution to a Stieltjes moment problem and constructs a family of coherent states for a charged particle in a magnetic field, including their mathematical properties and quantization implications.

Contribution

It introduces a novel approach to construct coherent states considering the circle topology of classical motion, linking moment problems with quantum state construction.

Findings

Constructed overcomplete, normalized coherent states

Proved the states solve the identity operator

Developed a Fock-Bergmann representation for quantization

Abstract

A solution to a version of the Stieltjes moment problem is presented. Using this solution, we construct a family of coherent states of a charged particle in a uniform magnetic field. We prove that these states form an overcomplete set that is normalized and solves the identity. By the help of the coherent states we construct the Fock-Bergmann representation related to the particle quantization. This quantization procedure takes into account a circle topology of the classical motion.