2 . 1 The gauge - invariant effective action for the Standard Model

The application of the background-field method to the electroweak Standard Model and its virtues are reviewed. Special emphasis is directed to the Ward identities that follow from the gauge invariance of the background-field effective action. They are compatible with on-shell renormalization and imply a decent behavior of the background-field vertex functions. Via the usual construction of connected Green functions they transfer to Ward identities for connected Green functions which, in distinction to the conventional formalism, remain exactly valid in finite orders of perturbation theory even if a Dyson summation of self-energies (within a systematic use of one-particle irreducible building blocks) is performed. Finally, we comment on the interplay between gauge invariance and gauge-parameter (in-)dependence of vertex and Green functions and the uniqueness of resummation procedures. Lecture given by G. Weiglein at the XXXVI Cracow School of Theoretical Physics, Zakopane, Poland, June 1–10, 1996. Partially supported by the EC-network contract CHRX-CT94-0579.