Five-dimensional Hamiltonian-Jacobi approach to relativistic quantum mechanics

Journal Article · Thu Dec 11 04:00:00 EST 2003 · Advances in Imaging and Electron Physics

OSTI ID:837739

Rose, Harald ^[1]

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1. LBNL Library

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.

• Research Organization: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• Sponsoring Organization: USDOE Director. Office of Science. Office of Basic Energy Sciences (US)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 837739
• Report Number(s): LBNL--54190
• Journal Information: Advances in Imaging and Electron Physics, Journal Name: Advances in Imaging and Electron Physics Vol. 132
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CLASSICAL MECHANICS
DIMENSIONS
DIRAC EQUATION
ELECTROMAGNETIC FIELDS
ELECTRONS
GRAVITATION
HAMILTON-JACOBI EQUATIONS
HAMILTONIAN-JACOBI RELATIVISTIC QUANTUM MECHANICS
INTEGRAL EQUATIONS
LAGRANGIAN FUNCTION
PATH INTEGRALS
POSITRONS
PROBABILITY
PROPAGATOR
QUANTIZATION
QUANTUM MECHANICS
SPIN
SPINORS
WAVE EQUATIONS