FM 13-2012 [Int. J. Mod. Phys. B, 26, 1244006 (2012)
SPECIAL ISSUE on Sixty Years of Luttinger Model: New Directions.
Guest Editors: D.Mattis, V.Mastropietro]

Author: Vieri Mastropietro

Title: Luttinger model and Luttinger liquids
Abstract: The Luttinger model owes its solvability to a number of peculiar features, like its linear relativistic dispersion relation, which are absent in more realistic fermionic systems. Nevertheless according to the Luttinger liquid conjecture a number of relations between exponents and other physical quantities, which are valid in the Luttinger model, are believed to be true in a wide class of systems, including tight binding or jellium one-dimensional fermionic systems. Recently a rigorous proof of several Luttinger liquid relations in nonsolvable models has been achieved; it is based on exact Renormalization Group methods coming from Constructive Quantum Field Theory and its main steps will be reviewed below.

Keywords: 1D interacting fermions, Luttinger liquid conjecture, constructive quantum field theory, renormalization group

Vieri Mastropietro
Dipartimento di Matematica
Università di Milano
Via Saldini, 50, I-20133 Milano - ITALY
e-mail: Vieri DOT Mastropietro AT unimi DOT it