Gaussian effective potential for the standard model SU(2)xU(1) electroweak theory

Understand

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.