Methods on compositeness and related aspects

TL;DR

This paper reviews methods for determining whether bound states and resonances are elementary or composite in quantum systems, focusing on calculating compositeness and addressing complex values for resonances.

Contribution

It introduces and discusses methods for calculating the compositeness of bound states and resonances in quantum mechanics and quantum field theory, including phase transformation techniques.

Findings

Methods for calculating compositeness in quantum systems.

Handling complex compositeness for resonances.

Application of phase transformations in S matrix analysis.

Abstract

In many physical applications, bound states and/or resonances are observed, which raises the question whether these states are elementary or composite. Here we elaborate on several methods for calculating the compositeness $X$ of bound states and resonances in Quantum Mechanics, and in Quantum Field Theory by introducing particle number operators. For resonances $X$ is typically complex and we discuss how to get meaningful results by using certain phase transformations in the $S$ matrix.