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arXiv · 2408.01770

Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian

Alexander J. Silenko
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Abstract

For Dirac particles interacting with external fields, we use the exact operator of the Foldy-Wouthuysen transformation obtained by Eriksen and rigorously derive a leading correction in the weak-field approximation to the known relativistic Foldy-Wouthuysen Hamiltonian. For this purpose, we carry out the operator extraction of a square root in the Eriksen operator. The derived correction is important for the scattering of relativistic particles. Since the description of this scattering by a relativistic wave equation of the second order is more convenient, we determine a general connection between relativistic wave equations of the first and second orders. For Dirac particles, the relativistic wave equation of the second order is obtained with a correction similar to that to the Foldy-Wouthuysen Hamiltonian.

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Alexander J. Silenko. 2024-08-03. Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian. https://doi.org/10.1103/physreva.111.032210

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