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A completely Lorentz-invariant Bohmian model has been proposed recently forthe case of a system of non-interacting spinless particles, obeyingKlein-Gordon equations. It is based on a multi-temporal formalism and on theidea of treating the squared norm of the wave function as a space-timeprobability density. The particle's configurations evolve in space-time interms of a parameter {\sigma}, with dimensions of time. In this work this modelis further analyzed and extended to the case of an interaction with an externalelectromagnetic field. The physical meaning of {\sigma} is explored. Twospecial situations are studied in depth: (1) the classical limit, where theEinsteinian Mechanics of Special Relativity is recovered and the parameter{\sigma} is shown to tend to the particle's proper time; and (2) thenon-relativistic limit, where it is obtained a model very similar to the usualnon-relativistic Bohmian Mechanics but with the time of the frame of referencereplaced by {\sigma} as the dynamical temporal parameter.

Classical and Non-Relativistic Limits of a Lorentz-Invariant Bohmian Model for a System of Spinless Particles