Dyson summation without violating Ward identities and the Goldstone-boson equivalence theorem

In contrast with the conventional treatment of gauge theories, in the background-field method the Ward identities for connected Green functions are not violated by Dyson summation of self-energies in finite orders of perturbation theory. Thus, Dyson summation does not spoil gauge cancellations at high energies which are ruled by the Goldstone-boson equivalence theorem. Moreover, in the background-field method the precise formulation of the equivalence theorem in higher orders (including questions of renormalization) is simplified rendering actual calculations easier. Finally, the equivalence theorem is also formulated for the standard model with a nonlinearly realized scalar sector and for the gauged nonlinear $\sigma$ model.