The zig-zag road to reality

TL;DR

This paper explores a pilot-wave quantum field theory for massless fermions, proposing a zig-zag electron model and suggesting that attributing beables to massless Dirac particles offers a more natural framework.

Contribution

It develops a pilot-wave theory for massless fermions using Weyl spinors and introduces a zig-zag electron model, enhancing understanding of quantum non-equilibrium in the early universe.

Findings

A massive Dirac electron can be viewed as a superposition of Weyl particles.

Single massive Dirac electrons can move luminally at all times.

Attributing beables to massless Dirac particles is more natural in quantum field theory.

Abstract

In the standard model of particle physics, all fermions are fundamentally massless and only acquire their effective bare mass when the Higgs field condenses. Therefore, in a fundamental de Broglie-Bohm pilot-wave quantum field theory (valid before and after the Higgs condensation), position beables should be attributed to massless fermions. In our endeavour to build a pilot-wave theory of massless fermions, which would be relevant for the study of quantum non-equilibrium in the early universe, we are naturally led to Weyl spinors and to particle trajectories which give meaning to the `zig-zag' picture of the electron discussed recently by Penrose. We show that a positive-energy massive Dirac electron of given helicity can be thought of as a superposition of positive and negative energy Weyl particles of the same helicity and that a single massive Dirac electron can in principle move luminally at all times. This is however not true for the many body situation required by quantum field theory and we conclude that a more natural theory arises from attributing beable status to the positions of massless Dirac particles instead of to Weyl particles.