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Five-dimensional Hamiltonian-Jacobi approach to relativistic quantum mechanics [electronic resource].

Published
Washington, D.C. : United States. Dept. of Energy. Office of Basic Energy Sciences, 2003.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy.
Physical Description
35 pages : digital, PDF file
Additional Creators
Lawrence Berkeley National Laboratory, United States. Department of Energy. Office of Basic Energy Sciences, and United States. Department of Energy. Office of Scientific and Technical Information
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Summary
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.
Report Numbers
E 1.99:lbnl--54190
lbnl--54190
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Note
Published through SciTech Connect.
12/11/2003.
"lbnl--54190"
Advances in Imaging and Electron Physics 132 FT
Rose, Harald.
Funding Information
AC03-76SF00098
A580AP
View MARC record | catkey: 13825511