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The Semi-Classical Relativistic Darwin Potential for Spinning Particles in the Rest-Frame Instant Form: 2-Body Bound States with Spin 1/2 Constituents

D. Alba·H. Crater·L. Lusanna
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Abstract

In the semiclassical approximation of Grassmann-valued electric charges for regularizing Coulomb self-energies, we extract the unique acceleration-independent interaction hidden in any Lienard-Wiechert solution for the system of N positive-energy spinning particles plus the electromagnetic field in the radiation gauge of the rest-frame instant form. With the help of a semiclassical Foldy-Wouthuysen transformation, this allows us to find the relativistic semiclassical Darwin potential. In the 2-body case the quantization of the lowest order reproduces exactly the results from the reduction of the Bethe-Salpeter equation.

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D. Alba, H. Crater, L. Lusanna. 2001-03-14. The Semi-Classical Relativistic Darwin Potential for Spinning Particles in the Rest-Frame Instant Form: 2-Body Bound States with Spin 1/2 Constituents. https://doi.org/10.1142/s0217751x0100430x

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