Where's that quantum?

TL;DR

This paper clarifies misconceptions about the vacuum and particle localization in quantum field theory, showing these issues are similar in non-relativistic systems and arise from misinterpretations of the vacuum and particles.

Contribution

It demonstrates that vacuum and localization issues are not unique to relativistic theories, providing a non-relativistic perspective and generalizing key theorems like Knight's.

Findings

Vacuum misinterpretation leads to misconceptions

Localization issues are analogous in non-relativistic systems

Reeh-Schlieder theorem implications are familiar from coupled oscillators

Abstract

The nature and properties of the vacuum as well as the meaning and localization properties of one or many particle states have attracted a fair amount of attention and stirred up sometimes heated debate in relativistic quantum field theory over the years. I will review some of the literature on the subject and will then show that these issues arise just as well in non-relativistic theories of extended systems, such as free bose fields. I will argue they should as such not have given rise either to surprise or to controversy. They are in fact the result of the misinterpretation of the vacuum as ``empty space'' and of a too stringent interpretation of field quanta as point particles. I will in particular present a generalization of an apparently little known theorem of Knight on the non-localizability of field quanta, Licht's characterization of localized excitations of the vacuum, and explain how the physical consequences of the Reeh-Schlieder theorem on the cyclicity and separability of the vacuum for local observables are already perfectly familiar from non-relativistic systems of coupled oscillators.