Foundations of Physics

, Volume 40, Issue 5, pp 532–544 | Cite as

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

  • Sergio Hernández-ZapataEmail author
  • Ernesto Hernández-Zapata


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.


Bohmian mechanics Klein-Gordon equation Relativistic quantum mechanics Multi-temporal formalism Space-time probability density Conditional wave function 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Sergio Hernández-Zapata
    • 1
    Email author
  • Ernesto Hernández-Zapata
    • 2
  1. 1.Facultad de CienciasUniversidad Nacional Autónoma de MéxicoDistrito FederalMéxico
  2. 2.Departamento de Física, Matemáticas e IngenieríaUniversidad de SonoraH. CaborcaMéxico

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