Algebraic bosonization: the study of the Heisenberg and Calogero-Sutherland models

Details Algebraic bosonization: the study of the Heisenberg and Calogero-Sutherland models Algebraic bosonization: the study of the Heisenberg and Calogero-Sutherland models

1996-03-16

arxiv.org/abs/hep-th/9603112v1

Int.J.Mod.Phys. A12 (1997) 4611-4661

Physics

High Energy Physics

High Energy Physics - Theory

51 pages, plain LaTeX

Scientific paper

10.1142/S0217751X97002498

We propose an approach to treat (1+1)--dimensional fermionic systems based on the idea of algebraic bosonization. This amounts to decompose the elementary low-lying excitations around the Fermi surface in terms of basic building blocks which carry a representation of the W_{1+\infty} \times {\overline W_{1+\infty}} algebra, which is the dynamical symmetry of the Fermi quantum incompressible fluid. This symmetry simply expresses the local particle-number current conservation at the Fermi surface. The general approach is illustrated in detail in two examples: the Heisenberg and Calogero-Sutherland models, which allow for a comparison with the exact Bethe Ansatz solution.

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