Universal Hidden Supersymmetry in Classical Mechanics and its Local Extension

TL;DR

This paper reviews a path-integral approach to classical mechanics revealing a universal hidden BRS invariance and supersymmetry, and extends these symmetries locally to understand their geometric significance.

Contribution

It uncovers a universal hidden BRS invariance and supersymmetry in classical mechanics and extends these symmetries locally, linking them to geometric structures on symplectic manifolds.

Findings

Identification of a universal hidden BRS invariance

Discovery of a universal hidden non-relativistic supersymmetry

Extension of supersymmetry to a local form with geometric interpretation

Abstract

We review here a path-integral approach to classical mechanics and explore the geometrical meaning of this construction. In particular we bring to light a universal hidden BRS invariance and its geometrical relevance for the Cartan calculus on symplectic manifolds. Together with this BRS invariance we also show the presence of a universal hidden genuine non-relativistic supersymmetry. In an attempt to understand its geometry we make this susy local following the analogous construction done for the supersymmetric quantum mechanics of Witten.