FM 00-3 ; mp_arc 00-??; nlin/CD 0001???

Author: Giovanni Gallavotti

Title: Renormalization group in Statistical Mechanics and Mechanics: gauge symmetries and vanishing beta functions.
 
Abstract: Two very different problems that can be studied by renormalization group methods are discussed with the aim of showing the conceptual unity that renormalization group has introduced in some areas of theoretical Physics. The two problems are: the ground state theory of a one dimensional quantum Fermi liquid and the existence of quasi periodic motions in classical mechanical systems close to integrable ones. I summarize here the main ideas and show that the two treatments, although completely independent of each other, are strikingly similar.

Keywords: Renormalization group, Fermi systems, KAM, Hamiltonian stability, Perturbation theory, Quantum fields

Giovanni Gallavotti                                 tel +39-06-4991-4370
Fisica, Universita' di Roma 1                  fax +39-06-4957697                    
P.le Moro 2                                         em giovanni.gallavotti@roma1.infn.it   
00185 Roma, Italia                                     http://ipparco.roma1.infn.it