Notes on Collective Field Theory of Matrix and Spin Calogero Models

TL;DR

This paper explores continuum, field theoretic representations of matrix and spin Calogero models using bosonization and collective field theory, comparing known methods and presenting new applications.

Contribution

It provides a comprehensive comparison of existing continuum representations and introduces novel applications of collective field theory to these models.

Findings

Multiple continuum representations are analyzed and compared.

New applications of collective field theory are demonstrated.

The models' relevance spans condensed matter, QCD, and string theory.

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.