Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian

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.

final version, 26 pages. arXiv admin note: text overlap with arXiv:1602.02246

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