THE W-1-SUTHERLAND MODEL AND LUTTINGER SYSTEMS(INFINITY EFFECTIVE THEORY OF THE CALOGERO)

We construct the effective field theory of the Calogero-Sutherland mod el in the thermodynamic limit of large number of particles N. It is gi ven by a W-1+infinity, conformal field theory (with central charge c = 1) that describes exactly the spatial density fluctuations arising fr om the low-energy excitations about the Fermi surface. Our approach do es not rely on the integrable character of the model, and indicates ho w to extend previous results to any order in powers of 1/N. Moreover, the same effective theory can also be used to describe an entire unive rsality class of (1+1)-dimensional fermionic systems beyond the Caloge ro-Sutherland model, which we identify with the class of chiral Luttin ger systems. We also explain how a systematic bosonization procedure c an be performed using the W-1+infinity, generators, and propose this a lgebraic approach to classify low-dimensional non-relativistic fermion ic systems, given that all representations of W-1+infinity, are known. This approach has the appeal of being mathematically complete and phy sically intuitive, encoding the picture suggested by Luttinger's theor em.