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