Notes on Collective Field Theory of Matrix and Spin Calogero Models

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.

arXiv comment36 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

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• Cold Fermi-gas with long range interaction in a harmonic trap
• Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries
• Nonlinear dynamics of spin and charge in spin-Calogero model
• Poisson Structures of Calogero-Moser and Ruijsenaars-Schneider Models
• Finiteness of Entanglement Entropy in Collective Field Theory
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Long Strings and Chiral Non-Singlets in Matrix Quantum Mechanics
• Waves and Solitons in the Calogero Model - Revisited