The Dirac Equation from a Bohmian Point of View

TL;DR

This paper develops a Lorentz-invariant Bohmian model for particles with spin, extending previous work on Klein-Gordon equations, and explores the classical limit and multi-particle systems.

Contribution

It introduces a Bohmian framework for spinor particles using Nikolic's probability density and synchronization, extending to two-particle covariant Dirac-like equations.

Findings

Classical limit obtained when spinor phases become equal as Planck's constant approaches zero.

Model successfully extends to two-particle systems with non-local covariant equations.

Provides a Lorentz-invariant Bohmian interpretation for spinor particles.

Abstract

In this paper we intend to extend some ideas of a recently proposed Lorentz-invariant Bohmian model, obeying Klein-Gordon equations, but considering particles with a spin different than zero. First we build a Bohmian model for a single particle, closely related to the Bohm-Dirac model, but using Nikolic's ideas on a space-time probability density and the introduction of a synchronization parameter \sigma for the particle trajectory. We prove that, in the case of a spinor whose component phases become equal when \plank \to 0, it is possible to use the usual Bohmian Mechanics procedures to obtain the classical limit. We extend these ideas for a two-particle system, based on two non-local but covariant Dirac-like equations.