Generalized Weyl quantization on the cylinder and quantum phase

TL;DR

This paper develops a generalized Weyl quantization framework for cylindrical phase space, enabling the representation of quantum observables related to phase in harmonic oscillators and electromagnetic fields as self-adjoint operators.

Contribution

It introduces a formalism for Weyl quantization on the cylindrical phase space, expanding the mathematical tools for quantum phase analysis.

Findings

Quantum observables for phase are represented by self-adjoint operators.

The formalism applies to harmonic oscillator and electromagnetic field phases.

Provides a consistent mathematical framework for phase quantization.

Abstract

Generalized Weyl quantization formalism for the cylindrical phase space $S^1 \times \mathbb{R}^1$ is developed. It is shown that the quantum observables relevant to the phase of linear harmonic oscillator or electromagnetic field can be represented within this formalism by the self-adjoint operators on the Hilbert space $L^2(S^1)$.