Wick product of white noise operators and quantum stochastic differential equations

Abstract

The Wick product of operators on Fock space is introduced on the basis of the analytic characterization theorem for operator symbols established within the framework of white noise distribution theory. Existence and uniqueness of solutions are proved for a certain class of ordinary differential equations for Fock space operators. Quantum stochastic differential equations of Itô type and their generalizations involving higher powers of quantum white noises enter into our consideration.