Report discussing the relationship between quantum field theory and the the statistical theory of waves. Basic equations exist in the latter theory which correspond closely to the fundamental equations of the former theory; i.e., to the commutation relations and the Heisenberg equation of motion. A probability density function of waves is introduced here which corresponds to the probability amplitude function in quantum mechanics. The theory of the statistical Green's functions and their relationships to the expectation values of the physical variables is also extensively developed. It is found that there exists a one-to-one correspondence between the formalism of Green's functions presented here and that used in field theory.