Antibrackets and Supersymmetric Mechanics

TL;DR

This paper develops a supergeneralization of Hamiltonian mechanics using odd symplectic structures, linking supersymmetric mechanics to geometric structures like Killing vectors and even symplectic forms.

Contribution

It introduces a novel supergeneralization framework for Hamiltonian mechanics based on odd symplectic structures and relates supersymmetric mechanics to Riemannian geometry.

Findings

Supergeneralization constructed using odd symplectic structure

Supersymmetric mechanics reformulated via even symplectic structure

Connection established between Killing vectors and supersymmetric mechanics

Abstract

Using odd symplectic structure constructed over tangent bundle of the symplectic manifold, we construct the simple supergeneralization of an arbitrary Hamiltonian mechanics on it. In the case, if the initial mechanics defines Killing vector of some Riemannian metric, corresponding supersymmetric mechanics can be reformulated in the terms of even symplectic structure on the supermanifold.