KAM Theorem and Quantum Field Theory

Details KAM Theorem and Quantum Field Theory KAM Theorem and Quantum Field Theory

1998-07-21

arxiv.org/abs/chao-dyn/9807029v1

Commun.Math.Phys. 201 (1999) 699-727

Physics

High Energy Physics

High Energy Physics - Theory

32 pages

Scientific paper

10.1007/s002200050573

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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