Higher order Lagrangian supermechanics

TL;DR

This paper extends higher order Lagrangian mechanics to the graded supermechanics setting using supervector fields and graded forms, and generalizes Noether's theorem within this framework.

Contribution

It introduces a graded geometric formalism for higher order Lagrangian supermechanics and proves a generalized version of Noether's theorem.

Findings

Extended higher order Lagrangian mechanics to graded supergeometry

Proved a generalized Noether's theorem in the supermechanics context

Developed a formalism using supervector fields and graded forms

Abstract

Using supervector fields and graded forms along a morphism, we study the geometry of ordinary differential superequations, extend the formalism of higher order Lagrangian mechanics to the graded context and prove a generalization of Noether's theorem.