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

Foundations of Physics 52 (5):1-13 (2022)
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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 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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Weak Values and Quantum Properties.A. Matzkin - 2019 - Foundations of Physics 49 (3):298-316.
Classical and Bohmian trajectories in semiclassical systems: Mismatch in dynamics, mismatch in reality?Alexandre Matzkin & Vanessa Nurock - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (1):17-40.

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