KAM Theorem and Quantum Field Theory

摘要

We give a new proof of the KAM theorem for analytic Hamiltonians. The proof is211u001einspired by a quantum field theory formulation of the problem and is based on a 211u001erenormalization group argument treating the small denominators inductively scale 211u001eby scale. The crucial cancellations of resonances are shown to follow from the 211u001eWard identities expressing the translation invariance of the corresponding field 211u001etheory.