Pilot-wave theory and quantum fields

TL;DR

This paper reviews and advances pilot-wave theories where quantum fields are described by additional variables called beables, focusing on field configurations for bosonic and fermionic fields, comparing different models and discussing their consistency with quantum predictions.

Contribution

It provides an overview and further development of pilot-wave theories for quantum fields, including comparisons between models for electromagnetic, scalar, and fermionic fields.

Findings

Bohm and Valentini's electromagnetic field theories are equivalent.

Holland's fermionic model needs further work to match quantum predictions.

Valentini's fermionic model faces unresolved issues.

Abstract

Pilot-wave theories provide possible solutions to the measurement problem. In such theories, quantum systems are not only described by the state vector, but also by some additional variables. These additional variables, also called beables, can be particle positions, field configurations, strings, etc. In this paper we focus our attention on pilot-wave theories in which the additional variables are field configurations. The first such theory was proposed by Bohm for the free electromagnetic field. Since Bohm, similar pilot-wave theories have been proposed for other quantum fields. The purpose of this paper is to present an overview and further development of these proposals. We discuss various bosonic quantum field theories such as the Schroedinger field, the free electromagnetic field, scalar quantum electrodynamics and the Abelian Higgs model. In particular, we compare the pilot-wave theories proposed by Bohm and by Valentini for the electromagnetic field, finding that they are equivalent. We further discuss the proposals for fermionic fields by Holland and Valentini. In the case of Holland's model we indicate that further work is required in order to show that the model is capable of reproducing the standard quantum predictions. We also consider a similar model, which does not seem to reproduce the standard quantum predictions. In the case of Valentini's model we point out a problem that seems hard to overcome.