On the Geometry of Supersymmetric Quantum Mechanical Systems

TL;DR

This paper explores the geometric interpretation of supersymmetric quantum mechanical systems using Clifford algebras, leading to extensions to higher dimensions and more complex potentials.

Contribution

It introduces a geometric framework for supersymmetric quantum systems based on Clifford algebras, enabling natural higher-dimensional generalizations.

Findings

Clifford algebra provides a geometric interpretation of supersymmetry.

Extensions to higher dimensions are systematically constructed.

Potential for analyzing more complex supersymmetric systems.

Abstract

We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the considered systems to higher dimensions and more complicated potentials.