The Weyl -- Wigner -- Moyal Formalism on a Discrete Phase Space. II. The Photon Wigner Function

TL;DR

This paper develops a quantum phase space framework for photons, introducing a photon Wigner function and exploring the quantum mechanics of light using the Weyl--Wigner--Moyal formalism on a discrete phase space.

Contribution

It constructs and interprets a photon Wigner function within the Weyl--Wigner--Moyal formalism, extending phase space quantum mechanics to photon states.

Findings

Photon Wigner function is explicitly constructed.

Quantum light can be described on a phase space using this formalism.

The approach provides new insights into photon quantum mechanics.

Abstract

Classical model of light in helicity formalism is presented. Then quantum point of view at photons -- construction and interpretation of photon wave function is proposed. Quantum mechanics of photon is investigated. The Bia\l ynicki -- Birula scalar product $\langle {\bf \Psi}_{1}|{\bf \Psi}_{2}\rangle_{BB}$ and the generalized Hermitian conjugation $\widehat{\gamma}^{+\hspace{-0.45em}+}$ of linear operator $\widehat{\gamma}$ are discussed. Quantum description of light on a phase space is developed. A photon Wigner function is built.