Calogero-Moser Models V: Supersymmetry and Quantum Lax Pair

TL;DR

This paper demonstrates the supersymmetrization of Calogero-Moser models across all root systems and potentials, providing universal formulas for ground states and establishing quantum Lax pairs and conserved quantities.

Contribution

It introduces a universal supersymmetrization framework for Calogero-Moser models and derives explicit formulas for ground states and conserved quantities.

Findings

Universal supersymmetric ground state wavefunction formula

Quantum Lax pair operators established for all models

Conserved quantities identified for various potentials

Abstract

It is shown that the Calogero-Moser models based on all root systems of the finite reflection groups (both the crystallographic and non-crystallographic cases) with the rational (with/without a harmonic confining potential), trigonometric and hyperbolic potentials can be simply supersymmetrised in terms of superpotentials. There is a universal formula for the supersymmetric ground state wavefunction. Since the bosonic part of each supersymmetric model is the usual quantum Calogero-Moser model, this gives a universal formula for its ground state wavefunction and energy, which is determined purely algebraically. Quantum Lax pair operators and conserved quantities for all the above Calogero-Moser models are established.