Orbital angular momentum in phase space

A comprehensive theory of the Weyl–Wigner formalism for the canonical pair angle–angular momentum is presented. Special attention is paid to the problems linked to rotational periodicity and angular-momentum discreteness.

Research highlights
► We propose a comprehensive Weyl–Wigner formalism for the canonical pair angle-angular momentum.
► We present a simple and useful toolkit for the practitioner.
► We derive simple evolution equations in terms of a star product in the semiclassical limit.