A class of exactly soluble many-body Hamiltonians with the interaction of substance and boson field

A general class of model systems of quantum statistical mechanics representing substance coupled to a discrete spectrum of a quantized boson field is studied on the basis of the “approximating (trial) Hamiltonian” method. Proof is presented that the models under investigation are exactly soluble in the thermodynamical limit. Besides, some characteristic features of the phase transitions in such systems are under consideration. Some concrete models are treated as an illustration.