A new class of Matrix Models arising from the W-infinity Algebra

Abstract

We present a new class of hermitian one-matrix models originated in the W-infinity algebra: more precisely, the polynomials defining the W-infinity generators in their fermionic bilinear form are shown to expand the orthogonal basis of a class of random hermitian matrix models. The corresponding potentials are given, and the thermodynamic limit interpreted in terms of a simple plasma picture. The new matrix models can be successfully applied to the full bosonization of interesting one-dimensional systems, including all the perturbative orders in the inverse size of the system. As a simple application, we present the all-order bosonization of the free fermionic field on the one-dimensional lattice.

8 pages, 1 figure

References in corpus (7)

• One-Dimensional Fermi liquids
• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• The $W_{1+\infty }$ effective theory of the Calogero- Sutherland model and Luttinger systems.
• Algebraic bosonization: the study of the Heisenberg and Calogero-Sutherland models
• Solving the Frustrated Spherical Model with q-Polynomials
• The extended conformal theory of Luttinger systems
• Extended conformal symmetry of the one-dimensional Bose gas