Generalized Weyl quantization on the cylinder and quantum phase

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 $L^2(S^1)$.