Non linear $\sigma$ models : renormalisability versus geometry

Abstract

After some recalls on the standard (non)-linear $\sigma$ model, we discuss the interest of B.R.S. symmetry in non-linear $\sigma$ models renormalisation. We also emphasise the importance of a correct definition of a theory through physical constraints rather than as given by a particular Lagrangian and discuss some ways to enlarge the notion of renormalisability.

10 pages, latex file, Talk given in Cortona, Italy, at the 1st June meeting in honnor of Carlo Becchi 60th birthday