Gauge-invariant effective potentials and Higgs boson 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 boson mass.