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

Foundations of Physics 40 (5):532-544 (2010)

Abstract
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating the squared norm of the wave function as a space-time probability density. The particle’s configurations evolve in space-time in terms of a parameter σ with dimensions of time. In this work this model is further analyzed and extended to the case of an interaction with an external electromagnetic field. The physical meaning of σ is explored. Two special situations are studied in depth: (1) the classical limit, where the Einsteinian Mechanics of Special Relativity is recovered and the parameter σ is shown to tend to the particle’s proper time; and (2) the non-relativistic limit, where it is obtained a model very similar to the usual non-relativistic Bohmian Mechanics but with the time of the frame of reference replaced by σ as the dynamical temporal parameter
Keywords Bohmian mechanics  Klein-Gordon equation  Relativistic quantum mechanics  Multi-temporal formalism  Space-time probability density  Conditional wave function
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DOI 10.1007/s10701-010-9413-7
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Quantum Mechanics: Myths and Facts. [REVIEW]Hrvoje Nikolić - 2007 - Foundations of Physics 37 (11):1563-1611.

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