KAM theorem and quantum field theory

摘要

We give a new proof of the KAM theorem for analytic Hamiltonians. The proofis inspired by a quantum field theory formulation of the problem and is basedon a renormalization group argument treating the small denominators inductivelyscale by scale. The crucial cancellations of resonances are shown to followfrom the Ward identities expressing the translation invariance of thecorresponding field theory. Comment: 32 pages