Wiener-Itô decomposition of polynomial operators formed with boson quasi-free fields

AbstractOrthogonal polynomials, as a generalized notion of multiple Wiener integrals, are constructed on non-commuting operators of free boson fields in non-Fock states. The orthogonal polynomials form a continuum of notions whose special cases are Wick products in Fock states and Hermite polynomials of commuting operators of free fields generally in non-Fock states. Structures of orthogonal polynomials as operators or operator-valued distributions are given, and multiplication formulas and commutation relations are presented