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

• URL: http://arxiv.org/abs/2207.14646v1
• Date: Thu, 28 Jul 2022 17:41:20 GMT
• Title: Relativistic Bohmian trajectories and Klein-Gordon currents for spin-0 particles
• Authors: M. Alkhateeb and A. Matzkin
• Abstract summary: It is generally believed that the de Broglie-Bohm model does not admit a particle interpretation for massive relativistic spin-0 particles. 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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