Relativistic Quantum and Classical Mechanics in the Hilbert Space

Details Relativistic Quantum and Classical Mechanics in the Hilbert Space Relativistic Quantum and Classical Mechanics in the Hilbert Space

2011-07-26

arxiv.org/abs/1107.5139v1

Physics

Quantum Physics

Scientific paper

We present a formulation of relativistic classical and quantum mechanics in the Hilbert space with a linkage through the Ehrenfest quantization. We start with the covariant form of the Lorentz force and consistently derive the Dirac equation along its classical counterpart as a classical spinorial equation. This equation fills a missing link between relativistic quantum and classical mechanics and takes the role of the Koopmann-von Neumann equation in the relativistic regime.

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