ALGEBRAIC BOSONIZATION - THE STUDY OF THE HEISENBERG AND CALOGERO-SUTHERLAND MODELS

We propose an approach to treating (1 + 1)-dimensional fermionic syste ms based on the idea of algebraic bosonization. This amounts to decomp osing the elementary low-lying excitations around the Fermi surface in terms of basic building blocks carrying a representation of the W1+in finity x (W) over bar(1+infinity) algebra, which is the dynamical symm etry of the Fermi quantum incompressible fluid. This symmetry simply e xpresses the local particle number current conservation at the Fermi s urface. The general approach is illustrated in detail through two exam ples: the Keisenberg and Calogero-Sutherland models, which allow compa rison with the exact Bethe ansatz solution.