The Ontology of Compositeness Within Quantum Field Theory

TL;DR

This paper investigates the concept of compositeness in Quantum Field Theory, demonstrating its limitations and proposing an approximate notion near multi-particle thresholds, which impacts metaphysical debates about the fundamentality of objects.

Contribution

It shows the impossibility of a rigorous definition of compositeness in Quantum Field Theory and introduces an approximate notion near multi-particle thresholds.

Findings

No satisfactory exact definition of compositeness in QFT.

An approximate compositeness can be defined near multi-particle thresholds.

Rejecting compositeness addresses metaphysical issues about the fundamentality of objects.

Abstract

In this work, we attempt to define a notion of compositeness compatible with Quantum Field Theory. Considering the analytic properties of the S-matrix, we conclude that there is no satisfactory definition of compositeness compatible with Quantum Field Theory. Without this notion, one must claim that all bound states are equally fundamental, that is, one cannot rigorously claim that everyday objects are made of atoms or that atoms are made of protons and neutrons. I then show how an approximate notion of compositeness may be recovered in the regime where the mass of a bound state is close to a multi-particle threshold. Finally, we see that rejecting compositeness solves several of the "problems of everyday objects" encountered in an undergraduate metaphysics course.