Abstract
The classical limit of real Dirac theory is derived as the lowest-order contribution in\(\mathchar'26\mkern-10mu\lambda = \hslash /mc\) of a new, exact polar decomposition. The resulting classical spinor equation is completely integrated for stationary solutions to arbitrary central fields. Imposing single-valuedness on the covering space of a bivector-valued extension to these classical solutions, orbital angular momentum, energy, and spin directions are quantized. The quantization of energy turns out to yield the WKB formula of Bessey, Uhlenbeck, and Good. It is demonstrated that the success of Sommerfeld's old quantization is due to a complete mutual cancellation between wave mechanical half-integers and spin in the particular case of the relativistic Kepler problem.
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Krüger, H. Classical limit of real Dirac theory: Quantization of relativistic central field orbits. Found Phys 23, 1265–1288 (1993). https://doi.org/10.1007/BF01883679
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DOI: https://doi.org/10.1007/BF01883679