An invariant renormalisation method for non-linear realisations of dynamical symmetries

Abstract

The structure of the ultraviolet divergence is investigated for the field theoretical models with non-linear realisation of an arbitrary semi-simple Lie group, with spontaneously broken symmetry of vacuum. An invariant formulation of the background-field method of renormalisation is proposed which gives the manifestly invariant counter-terms off mass shell. A simple algorithm for construction of counter-terms is developed. It is based on invariants of the group of dynamical symmetry in terms of the Cartan forms. The results of one-loop and two-loop calculations are reported.