In 2004 Oliveira et al. developed a new wave-function formalism in phase space where the wave-function is associated to the Wigner quasiprobability distribution by means of the Moyal product. An advantage might be that off-diagonal Wigner functions used in superpositions are treated in an intuitive way, ψ ψ 1 ⋆ ⋆ ψ ψ 2 , also gauge theories are treated in an operator form.