Positive Quantization in the Presence of a Variable Magnetic Field

TL;DR

This paper develops a Berezin quantization framework for particles in variable magnetic fields, extending coherent states and phase-space analysis to include magnetic effects, resulting in a strict quantization of the associated Poisson algebra.

Contribution

It introduces a novel Berezin quantization method incorporating variable magnetic fields, expanding the mathematical tools for quantum systems with magnetic interactions.

Findings

Establishes a magnetic Berezin quantization as a strict quantization.

Develops a magnetic Bargmann space framework.

Connects Berezin-Toeplitz operators with magnetic phase-space analysis.

Abstract

Starting with a previously constructed family of coherent states, we introduce the Berezin quantization for a particle in a variable magnetic field and we show that it constitutes a strict quantization of a natural Poisson algebra. The phase-space reinterpretation involves a magnetic version of the Bargmann space and leads naturally to Berezin-Toeplitz operators.