On the "Universal" N=2 Supersymmetry of Classical Mechanics

TL;DR

This paper explores a local N=2 supersymmetry in classical mechanics, its geometric features, and its relation to ergodicity, revealing how constraints on energy surfaces affect the supersymmetry structure.

Contribution

It clarifies the geometric nature of a universal N=2 supersymmetry in classical mechanics and investigates its interplay with ergodicity and energy surface constraints.

Findings

Local Grassmannian invariances emerge on energy surfaces

N=2 supersymmetry reduces to N=1 under constraints

Provides pedagogical clarification of supersymmetry in classical systems

Abstract

In this paper we continue the study of the geometrical features of a functional approach to classical mechanics proposed some time ago. In particular we try to shed some light on a N=2 "universal" supersymmetry which seems to have an interesting interplay with the concept of ergodicity of the system. To study the geometry better we make this susy local and clarify pedagogically several issues present in the literature. Secondly, in order to prepare the ground for a better understanding of its relation to ergodicity, we study the system on constant energy surfaces. We find that the procedure of constraining the system on these surfaces injects in it some local grassmannian invariances and reduces the N=2 global susy to an N=1.