Relativistic Bohmian Trajectories and Klein-Gordon Currents for Spin-0 Particles

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 Klei...

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Bibliographic Details
Published in:Foundations of physics 2022-10, Vol.52 (5), Article 104
Main Authors: Alkhateeb, M., Matzkin, A.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Classical Mechanics
Density currents
History and Philosophical Foundations of Physics
Klein-Gordon equation
Particle spin
Particle trajectories
Philosophy of Science
Physics
Physics and Astronomy
Quantum Physics
Relativistic effects
Relativistic particles
Relativity Theory
Representations
Statistical Physics and Dynamical Systems
Velocity distribution
Wave functions
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Summary: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.
ISSN:0015-9018
1572-9516
DOI:10.1007/s10701-022-00625-2