The Luttinger model: Its role in the RG-theory of one dimensional many body Fermi systems

The Luttinger model was introduced to illustrate the possibility of a pertu rbative treatment of the singularity at the Fermi surface, already known to be "anomalous" from the results of the theory of Tomonaga, via an exactly soluble model. It became soon the subject of great interest also on the par t of Mathematical Physics and a key to the investigations of the mathematic al properties of Condensed Matter Physics. This paper reviews aspects of th e above developments relevant for renormalization group methods by illustra ting the conceptual development of the renormalization group approach to th e ground state theory of the 1-dimensional spinless Fermi gas at small coup ling.