  I consider the case of two interacting scalar fields, \phi and \psi, and use
the path integral formalism in order to treat the first classically and the
second quantum-mechanically. I derive the Feynman rules and the resulting
equation of motion for the classical field, which should be an improvement of
the usual semi-classical procedure. As an application I use this method in
order to enforce Gauss's law as a classical equation in a non-abelian gauge
theory. I argue that the theory is renormalizable and equivalent to the usual
Yang-Mills as far as the gauge field terms are concerned. There are additional
terms in the effective action that depend on the Lagrange multiplier field
\lambda that is used to enforce the constraint. These terms and their relation
to the confining properties of the theory are discussed.
