Canonical derivation of effective potentials

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.