  The parametric equations of KAM tori for a quasi integrable system, are shown
to be one point Schwinger functions of a suitable euclidean quantum field
theory on the torus. KAM theorem is equivalent to a ultraviolet stability
theorem. A renormalization group treatment of the field theory leads to a
resummation of the formal pertubation series and to an expansion in terms of
new parameters (identified as a family of renormalization constants). The new
parameters are analytic in the coupling (at small coupling): the breakdown of
the tori at large coupling is speculated to be related to the crossing of a
"critical" surface at a value where the renormalization constants are still
finite. 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 coupling dependence, is proposed.}
