  A canonical formulation of effective equations describes quantum corrections
by the back-reaction of moments on the dynamics of expectation values of a
state. As a first step toward an extension to quantum-field theory, these
methods are applied here to the derivation of effective potentials around a
homogeneous vacuum expectation value of scalar fields. A comparison with the
standard Coleman-Weinberg potential shows that the new methods correctly
include all relevant quantum corrections. At the same time, the effective
potential is shown to be correct also for non-Fock and mixed states. Several
explicit results are derived in models of interacting scalars and fermions.
