Further developments of the covariant functional formalism for interacting fields. - III

In this work the covariant functional formalism developped in two previous articles is extended to the case of coupled boson fields and of fermion fields, either free or coupled to boson fields. The sufficiency of the knowledge of the energy in order to determine the evolution of coupled fields is discussed, and some properties of the state vector, resulting immediately from the covariant functional formulation in the Schrodinger representation, are given. It is shown that at the classical limit (ħ → 0), the solution of the equations of motion for coupled fields exists and is unique.