FM 2000-11      mp_arc@math.utexas.edu \# NO
                cond-mat@xyz.lanl.gov  \# NO

Authors: Guido Gentile, Vieri Mastropietro

Title: Renormalization Group for one-dimensional fermions.
       A review on mathematical results

Abstract: In this work we shall review what is known at a rigorous
level about the correlation functions of many (generally not soluble)
models of interacting one-dimensional Fermi systems, with emphasis
about the new results obtained starting from the '90.  A main novelty
is the application to solid state models of the techniques based on
the rigorous implementation of Wilsonian Renormalization Group,
developed in the context of constructive Quantum Field Theory.  Such
techniques allow in principle to express the correlation functions of
a quantum field theory describing Fermi systems as convergent series
(even if they are generally non-analytic in the perturbative
parameters).  Aim of this paper is from one side to review in a
systematic way results spreaded out in a number of works and from the
other to provide the technical tools necessary to read the original
papers.

Keywords: Renormalization Group, Quantum Field Theory,
One-Dimensional Fermi Systems, Correlation functions,
Schwinger functions, Functional Integral

Addresses:

G.G.: Matematica, Universita' di Roma 3,
        Largo S. Leonardo Murialdo, 1, 00146, Roma, Italia
V.M.: Matematica, Universita' di Roma 2,
        Viale della Ricerca Scientifica, 00133, Roma, Italia.

e-mail: mastropi@mat.uniroma2.it
        gentile@matrm3.mat.uniroma3.it