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KAM Theorem and Quantum Field Theory

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Abstract:

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

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Authors and Affiliations

  1. UCL, FYMA, 2 chemin du Cyclotron, B-1348 Louvain-la-Neuve, Belgium, , , , , , BE

    Jean Bricmont

  2. CNRS, IHES, 35 route de Chartres, 91440 Bures-sur-Yvette, France, , , , , , FR

    Krzysztof Gawędzki

  3. Department of Mathematics, Helsinki University, P.O. Box 4, 00014 Helsinki, Finland, , , , , , FI

    Antti Kupiainen

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  1. Jean Bricmont
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  2. Krzysztof Gawędzki
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  3. Antti Kupiainen
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Received: Received: 23 July 1998 / Accepted: 23 September 1998

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Bricmont, J., Gawędzki, K. & Kupiainen, A. KAM Theorem and Quantum Field Theory. Comm Math Phys 201, 699–727 (1999). https://doi.org/10.1007/s002200050573

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  • DOI: https://doi.org/10.1007/s002200050573

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