The topological meaning of Levinson's theorem, half-bound states included

TL;DR

This paper interprets Levinson's theorem as a topological index theorem, providing a deeper understanding of its nature and clarifying the role of resonances at thresholds.

Contribution

It introduces a topological interpretation of Levinson's theorem, linking it to index theory and explaining threshold resonance corrections coherently.

Findings

Levinson's theorem can be viewed as an index theorem.

Resonance corrections at thresholds are explained topologically.

Provides a unified framework for understanding half-bound states.

Abstract

We propose to interpret Levinson's theorem as an index theorem. This exhibits its topological nature. It furthermore leads to a more coherent explanation of the corrections due to resonances at thresholds.