On the geometric arena of supermechanics

TL;DR

This paper explores the geometric framework of supermechanics using graded manifolds, focusing on the representation of supervector fields and superforms as sections of vector bundles.

Contribution

It provides a geometric interpretation of supervector fields and superforms within the context of graded manifolds in supermechanics.

Findings

Supervector fields are represented by sections of smooth vector bundles.

Exterior superforms are described as sections of vector bundles.

The geometric approach clarifies the structure of supermechanics.

Abstract

In the case of simple graded manifolds utilized in supermechanics, supervector fields and exterior superforms are represented by global sections of smooth vector bundles.