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

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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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Notes

  1. This expression was first obtained in Ref. [17]; see [18] for a brief review on weak values, including a discussion on the current density.

  2. De Broglie wittingly notes the similarity between his reasoning and Bohr’s argumentation, see p. 135 in [23].

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  1. Laboratoire de Physique Théorique et Modélisation, CNRS Unité 8089, CY Cergy Paris Université, Cedex 95302, Cergy-Pontoise, France

    M. Alkhateeb & A. Matzkin

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  1. M. Alkhateeb
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  2. A. Matzkin
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Alkhateeb, M., Matzkin, A. Relativistic Bohmian Trajectories and Klein-Gordon Currents for Spin-0 Particles. Found Phys 52, 104 (2022). https://doi.org/10.1007/s10701-022-00625-2

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