Hamiltonian systems of Calogero type and two dimensional Yang-Mills theory

TL;DR

This paper derives integral representations for Calogero-type wave functions, generalizes these to Kac-Moody algebras, and explores their connections with two-dimensional Yang-Mills theory and the Generalized Kontsevich Model.

Contribution

It introduces a novel integral representation for Calogero systems, extends the framework to Kac-Moody algebras, and links these models to 2D Yang-Mills theory and the Kontsevich Model.

Findings

Integral representations for Calogero wave functions derived

Connections established between Calogero models and 2D Yang-Mills theory

Large k limit relates to the Generalized Kontsevich Model

Abstract

We obtain integral representations for the wave functions of Calogero-type systems,corresponding to the finite-dimentional Lie algebras,using exact evaluation of path integral.We generalize these systems to the case of the Kac-Moody algebras and observe the connection of them with the two dimensional Yang-Mills theory.We point out that Calogero-Moser model and the models of Calogero type like Sutherland one can be obtained either classically by some reduction from two dimensional Yang-Mills theory with appropriate sources or even at quantum level by taking some scaling limit.We investigate large k limit and observe a relation with Generalized Kontsevich Model.