The Fundamentality of Fields

TL;DR

This paper advocates for a field-based interpretation of quantum field theory, highlighting its advantages over a particle approach, and discusses key challenges for proponents of the field perspective.

Contribution

It presents three main advantages of the field approach over the particle approach and outlines two critical tasks for advancing the field interpretation.

Findings

Field approach better accounts for photons, spin, and self-interaction.

Space of field wave functionals is larger than that of particle wave functions.

Highlights challenges in justifying Grassmann numbers and explaining particle emergence.

Abstract

There is debate as to whether quantum field theory is, at bottom, a quantum theory of fields or particles. One can take a field approach to the theory, using wave functionals over field configurations, or a particle approach, using wave functions over particle configurations. This article argues for a field approach, presenting three advantages over a particle approach: (1) particle wave functions are not available for photons, (2) a classical field model of the electron gives a superior account of both spin and self-interaction as compared to a classical particle model, and (3) the space of field wave functionals appears to be larger than the space of particle wave functions. The article also describes two important tasks facing proponents of a field approach: (1) legitimize or excise the use of Grassmann numbers for fermionic field values and in wave functional amplitudes, and (2) describe how quantum fields give rise to particle-like behavior.