Field Theory and Kam Tori

The parametric equations of KAM tori for a l degrees of freedom quasi integrable system, are shown to be one point Schwinger functions of a suitable euclidean quantum eld theory on the l dimensional torus. KAM theorem is equivalent to a ultraviolet stability theorem. A renormalization group treatment of the eld theory leads to a resummation of the formal pertubation series and to an expansion in terms of l 2 new parameters forming a l l matrix " (identiied as a family of renormalization constants). The matrix " is an analytic function of the coupling " at small ": the breakdown of the tori at large " is speculated to be related to the crossing by " of a \critical" surface at a value " = " c where the function " is still nite. A mechanism for the possible universality of the singularities of parametric equations for the invariant tori, in their parameter dependence as well as in the " c ? " dependence, is proposed.