Related papers: Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian

Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian

URL: http://arxiv.org/abs/2408.01770v2
Date: Fri, 27 Sep 2024 09:20:12 GMT
Title: Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian
Authors: Alexander J. Silenko,
Abstract summary: We rigorously derive a leading correction in the weak-field approximation to the known relativistic Foldy-Wouthuysen Hamiltonian. For Dirac particles, the relativistic wave equation of the second order is obtained with the correction similar to that to the Foldy-Wouthuysen Hamiltonian.
Score: 55.2480439325792
License: http://creativecommons.org/licenses/by/4.0/
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 the correction similar to that to the Foldy-Wouthuysen Hamiltonian.

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