The Weyl - Wigner - Moyal formalism on a discrete phase space. II. The photon Wigner function

Classical model of light in helicity formalism is presented. Then a quantum mechanical point of view on photons—the construction and interpretation of two equivalent photon wave functions—is proposed. Quantum mechanics of the photon is investigated. The Białynicki–Birula scalar product $⟨\Psi 1|\Psi 2⟩{\mathrm{B\; B}}_{}$ and the generalized Hermitian conjugation ${\mathrm{\gamma ̂}}^{++}$ of a linear operator $\mathrm{\gamma ̂}$ are discussed. A quantum description of light on phase space based on the Weyl–Wigner–Moyal approach is developed. A photon Wigner function is constructed. Some explicit photon Wigner functions for different kernels are obtained. (© 2020 Wiley-VCH GmbH)