On a conjectured property of the Witten index and an application to Levinson's theorem

TL;DR

This paper investigates a conjectured property of the Witten index, establishing a composition rule and applying it to Levinson's theorem to deepen understanding of topological invariants in quantum systems.

Contribution

It proves a composition rule for the Witten index and demonstrates its application to Levinson's theorem, advancing the theoretical framework of topological invariants.

Findings

Established a composition rule for the Witten index

Applied the rule to derive implications for Levinson's theorem

Enhanced understanding of topological invariants in quantum physics

Abstract

A few years ago Fritz Gesztesy raised the issue of whether there was a composition rule for the Witten index analogous to that satisfied by Fredholm operators. In this note we prove a result in this direction and provide an application to Levinson's theorem.