Derivation of model Hamiltonians for interacting subsystems of nonidentical particles

A method is given for deriving model Hamiltonians which describe the behavior of a subsystem in interaction with a set of different particles. The formalism is illustrated by reducing the Jaynes-Cummings Hamiltonian for an interacting fermion-boson system, to a fermion-only Hamiltonian. The conditions are discussed under which such elimination of degrees of freedom is possible.