KAM Theorem and Quantum Field Theory
chao-dyn
2009-10-31 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Chaotic Dynamics
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.
Keywords
Cite
@article{arxiv.chao-dyn/9807029,
title = {KAM Theorem and Quantum Field Theory},
author = {J. Bricmont and K. Gawedzki and A. Kupiainen},
journal= {arXiv preprint arXiv:chao-dyn/9807029},
year = {2009}
}
Comments
32 pages