Five-dimensional Hamiltonian-Jacobi approach to relativistic quantum mechanics

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A novel theory is outlined for describing the dynamics of relativistic electrons and positrons. By introducing the Lorentz-invariant universal time as a fifth independent variable, the Hamilton-Jacobi formalism of classical mechanics is extended from three to four spatial dimensions. This approach allows one to incorporate gravitation and spin interactions in the extended five-dimensional Lagrangian in a covariant form. The universal time has the function of a hidden Bell parameter. By employing the method of variation with respect to the four coordinates of the particle and the components of the electromagnetic field, the path equation and the electromagnetic field produced by ... continued below

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35 pages; OS: Win90

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Rose, Harald December 11, 2003.

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A novel theory is outlined for describing the dynamics of relativistic electrons and positrons. By introducing the Lorentz-invariant universal time as a fifth independent variable, the Hamilton-Jacobi formalism of classical mechanics is extended from three to four spatial dimensions. This approach allows one to incorporate gravitation and spin interactions in the extended five-dimensional Lagrangian in a covariant form. The universal time has the function of a hidden Bell parameter. By employing the method of variation with respect to the four coordinates of the particle and the components of the electromagnetic field, the path equation and the electromagnetic field produced by the charge and the spin of the moving particle are derived. In addition the covariant equations for the dynamics of the components of the spin tensor are obtained. These equations can be transformed to the familiar BMT equation in the case of homogeneous electromagnetic fields. The quantization of the five-dimensional Hamilton-Jacobi equation yields a five-dimensional spinor wave equation, which degenerates to the Dirac equation in the stationary case if we neglect gravitation. The quantity which corresponds to the probability density of standard quantum mechanics is the four-dimensional mass density which has a real physical meaning. By means of the Green method the wave equation is transformed into an integral equation enabling a covariant relativistic path integral formulation. Using this approach a very accurate approximation for the four-dimensional propagator is derived. The proposed formalism makes Dirac's hole theory obsolete and can readily be extended to many particles.

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35 pages; OS: Win90

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INIS; OSTI as DE00837739

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  • Journal Name: Advances in Imaging and Electron Physics; Journal Volume: 132; Other Information: Submitted to Advances in Imaging and Electron Physics: Volume 132; Journal Publication Date: 2004

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  • Report No.: LBNL--54190
  • Grant Number: AC03-76SF00098
  • Office of Scientific & Technical Information Report Number: 837739
  • Archival Resource Key: ark:/67531/metadc778647

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • December 11, 2003

Added to The UNT Digital Library

  • Dec. 3, 2015, 9:30 a.m.

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  • Sept. 21, 2017, 6:04 p.m.

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Rose, Harald. Five-dimensional Hamiltonian-Jacobi approach to relativistic quantum mechanics, article, December 11, 2003; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc778647/: accessed July 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.