Gauge Invariant Effective Potentials and Higgs Mass Bounds

The problem of defining a gauge invariant effective potential with a strict energetic interpretation is examined in the context of spontaneously broken gauge theories. It is shown that such a potential can be defined in terms of a composite gauge invariant order parameter in physical gauges. This effective potential is computed through one loop order in a model with scalars and fermions coupled to an abelian gauge theory, which serves as a simple model of the situation in electroweak theory, where vacuum stability arguments based on the scalar effective potential have been used to place lower bounds on the Higgs mass.