Relativistic Bohmian trajectories and Klein-Gordon currents for spin-0 particles

TL;DR

This paper demonstrates that by using a Foldy-Wouthuysen type representation, one can define well-behaved Bohmian trajectories and conserved currents for relativistic spin-0 particles described by the Klein-Gordon equation, challenging previous assumptions.

Contribution

It introduces a new approach using a Foldy-Wouthuysen type representation to define particle trajectories and currents for Klein-Gordon particles, enabling a particle interpretation.

Findings

Bohmian trajectories are well-behaved and sub-luminal.

A positive conserved density and current can be defined.

Standard velocity fields can take arbitrarily high values, but the new approach avoids this.

Abstract

It is generally believed that the de Broglie-Bohm model does not admit a particle interpretation for massive relativistic spin-0 particles, on the basis that particle trajectories cannot be defined. We show this situation is due to the fact that in the standard (canonical) representation of the Klein-Gordon equation the wavefunction systematically contains superpositions of particle and anti-particle contributions.\ We argue that by working in a Foldy-Wouthuysen type representation uncoupling the particle from the anti-particle evolutions, a positive conserved density for a particle and associated density current can be defined.\ For the free Klein-Gordon equation the velocity field obtained from this current density appears to be well-behaved and sub-luminal in typical instances. As an illustration, Bohmian trajectories for a spin-0 boson distribution are computed numerically for free propagation in situations in which the standard velocity field would take arbitrarily high positive and negative values.