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Primitive Quantization in the Relativistic Two-Body Problem
Phys. Rev. 89, 467 – Published 15 January, 1953
DOI: https://doi.org/10.1103/PhysRev.89.467
Abstract
A pair of events, one for each of two particles, is regarded as a point in 8-space (). The technique of Hamilton's optical method is applied to , giving rays and associated de Broglie waves. These waves are quantized by associating a phase-cycle with an increase of in the characteristic function, and hence quantum rules appear as resonance conditions on the de Broglie waves, when the part of occupied by rays is multiply connected. A Hamiltonian equation is written down, the interaction between the particles being taken to be of Coulomb form, but with ordinary distance replaced by Minkowskian separation. This leads without approximation to a simple expression for quantized proper energies of the system, and from this expression follow the correct approximate energy levels for the hydrogenic atom (with ), the mass-correction factor being included. There is no approximation based on smallness of relative velocity or ratio of masses, and mathematical complexities associated with retarded potentials are avoided by the use of the relativistic Coulomb interaction.
References (5)
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