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

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.

References in corpus (5)

• Position and spin in relativistic quantum mechanics
• Bohmian mechanics, the quantum-classical correspondence and the classical limit: the case of the square billiard
• Quantum Preferred Frame: Does It Really Exist?
• Relativistic time-dependent quantum dynamics across supercritical barriers for Klein-Gordon and Dirac particles
• Are Bohmian trajectories real? On the dynamical mismatch between de Broglie-Bohm and classical dynamics in semiclassical systems