Mixed correlation functions in systems interacting with Bose fields

For a large class of systems interacting with Bose fields, exact expressions are found for correlation functions containing products of Bose operators with evolution law of the free field and operators of the “medium.” Hierarchical equations describing the evolution of the system are constructed by means of these expressions. The Born–Markov approximation is investigated. A “causality principle” associated with the absence of an influence on the evolution of the system of stochastic forces due to the free field at short times is established.