Notes on collective field theory of matrix and spin Calogero models

2006/07/31 by Inês Aniceto, Antal Jevicki · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #cond-mat.other #hep-th

paper · pdf · doi:10.1088/0305-4470/39/41/s06

published as J.Phys.A39:12765-12792,2006 · 36 pages, no figures v2: references added, a version to appear in the special issue of JPhysA (edited by G Dunne, J Feinberg and P Dorey) v3:comments changed, paper identical to v2

arxiv created 2006/09/01 · openalex publication_date 2006/09/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Matrix models and related Spin-Calogero-Sutherland models are of major relevance in a variety of subjects, ranging from condensed matter physics to QCD and low dimensional string theory. They are characterized by integrability and exact solvability. Their continuum, field theoretic representations are likewise of definite interest. In this paper we describe various continuum, field theoretic representations of these models based on bosonization and collective field theory techniques. We compare various known representations and describe some nontrivial applications.

Citations

• Solving the eigenvalue problem arising from the adjoint sector of the c=1 matrix model
• Quantum Hydrodynamics, Quantum Benjamin-Ono Equation, and Calogero Model
• An introduction to bosonization
• Dressing symmetries

Cited by

• Collective field formulation of the multi-species Calogero model and its duality symmetries
• Solitons and giants in matrix models
• Nonlinear dynamics of spin and charge in spin-Calogero model