  The Gaussian Effective Potential (GEP) is derived for the non-Abelian
SU(2)xU(1) gauge theory of electroweak interactions. First the problem of gauge
invariance is addressed in the Abelian U(1) theory, where an optimized GEP is
shown to be gauge invariant. The method is then extended to the full
non-Abelian gauge theory where, at variance with naive derivations, the GEP is
proven to be a genuine variational tool in any gauge. The role of ghosts is
discussed and the unitarity gauge is shown to be the only choice which allows
calculability without insertion of further approximations. The GEP for the
standard model is derived and its predictions are compared to the known
phenomenology, thus showing that the GEP provides an alternative
non-perturbative description of the known experimental data. By a consistent
renormalization of masses the full non-Abelian calculation confirms the
existence of a light Higgs boson in the non-perturbative strong coupling regime
of the Higgs sector.
