S-ordered Expansion of the Intermediate Representation Projector and Its Applications

Abstract

We first deduce the s-ordered expansion of the Wigner operator. Since Radon transformation of Wigner operator is just the intermediate representation |x λ,ν projector, we naturally obtain the s-ordered product of |x λ,νλ,ν x|. Accordingly, the completeness relation is still preserved under the s-ordering. Finally, based on it, we obtain the s-ordered expansion of some useful operator in quantum optics, and some new operator identities are revealed accordingly.