Non-linear renormalisation and the equivalence theorem

Abstract

The consequences of a field redefinition on the renormalisability character of a theory are thoroughly studied in the special example of the non-linear σ model in two dimensions. Using a minimal-dimensional method, we show that, although multiplicative renormalisability is lost, the divergences of the new field theory can be reabsorbed through a field-dependent renormalisation of the fields and, for the physical parameters, the same multiplicative renormalisation constants as in the original theory, to all orders of perturbation theory.