Pilot-wave theory and quantum fields

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 Schrödinger 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.1 Postdoctoral Fellow FWO. 2 Corresponding address.

Applied Bohmian mechanics

“…This mechanism allows effectively for the nonconservation of the particle's number in quantum systems. Particle's positions are usually the "hidden variables" in Bohmian mechanics but this is not mandatory [166]. Fields (or even strings) could be also taken as the hidden variables.…”

Lorentz-Invariant, Retrocausal, and Deterministic Hidden Variables

“…A possible extension concerns BM applied to bosonic quantum field. Following the Schrödinger-functional approach advocated by Bohm [3,11] (for reviews see [62,63]) a bosonic quantum field is described by the wave-functional The most known example is the scalar real field obeying to the Klein-Gordon equation and which is characterized for a foliation F 0 by the guidance equation [64,65,28]…”

Towards a Novel Approach to Semi-Classical Gravity

“…More specifically, we will consider bosonic quantum field theories. In Bohmian approaches to such theories it is most easy to introduce actual field variables rather than particle positions [6,15]. To illustrate how this works, let us consider the free massless real scalar field (for the treatment of other bosonic field theories see [15]).…”

“…In Bohmian approaches to such theories it is most easy to introduce actual field variables rather than particle positions [6,15]. To illustrate how this works, let us consider the free massless real scalar field (for the treatment of other bosonic field theories see [15]). Working in the functional Schrödinger picture, the quantum state vector is a wave functional Ψ(φ) defined on a space of scalar fields in 3-space and it satisfies the functional Schrödinger equation…”