Hamilton-Jacobi Mechanics from Pseudo-Supersymmetry

TL;DR

This paper demonstrates that solutions to the Hamilton-Jacobi equation can be extended to N=2 pseudo-supersymmetric systems, linking classical mechanics, supersymmetry, and cosmology through detailed examples.

Contribution

It introduces a novel connection between Hamilton-Jacobi solutions and pseudo-supersymmetry, providing a new framework for analyzing classical systems with supersymmetric structures.

Findings

Hamilton-Jacobi solutions define N=2 pseudo-supersymmetric extensions.

The momenta-Hamilton's principal function relation is a BPS condition.

Applications to relativistic/non-relativistic particles and cosmology.

Abstract

For a general mechanical system, it is shown that each solution of the Hamilton-Jacobi equation defines an N=2 pseudo-supersymmetric extension of the system, such that the usual relation of the momenta to Hamilton's principal function is the `BPS' condition for preservation of 1/2 pseudo-supersymmetry. The examples of the relativistic and non-relativistic particle, in a general potential, are worked through in detail, and used to discuss the relation to cosmology and to supersymmetric quantum mechanics.