Supersymmetry versus Integrability in two-dimensional Classical Mechanics

TL;DR

This paper explores how supersymmetry can be integrated into two-dimensional classical mechanical systems that are separable and integrable, revealing the relationship between supersymmetry and integrability.

Contribution

It introduces two independent methods to implement supersymmetry in Liouville systems and analyzes the resulting constants of motion.

Findings

Supersymmetry can be incorporated in two distinct ways.

The structure of constants of motion is clarified.

The relationship between supersymmetry and integrability is examined.

Abstract

Supersymmetric extensions of Hamilton-Jacobi separable Liouville mechanical systems with two degrees of freedom are defined. It is shown that supersymmetry can be implemented in this type of systems in two independent ways. The structure of the constants of motion is unveiled and the entanglement between integrability and supersymmetry is explored.