Description of identical particles via gauged matrix models : a generalization of the Calogero-Sutherland system

TL;DR

This paper proposes a framework using gauged matrix models to describe identical particles, generalizing the Calogero-Sutherland system by making the interaction strength dynamical and bounded below.

Contribution

It introduces a novel gauged matrix model approach that extends the Calogero-Sutherland system with a dynamical, bounded inverse square potential.

Findings

The model is exactly solvable.

It generalizes the inverse square potential to be dynamical.

The approach provides a natural description of identical particles.

Abstract

We elaborate the idea that the matrix models equipped with the gauge symmetry provide a natural framework to describe identical particles. After demonstrating the general prescription, we study an exactly solvable harmonic oscillator type gauged matrix model. The model gives a generalization of the Calogero-Sutherland system where the strength of the inverse square potential is not fixed but dynamical bounded by below.