Abstract
We carry out a direct iterative Foldy-Wouthuysen transformation of a general Dirac Hamiltonian coupled to an electromagnetic field, including the anomalous magnetic moment. The transformation is carried out through an iterative disentangling of the particle and antiparticle Hamiltonians in the expansion for higher orders of the momenta. The time-derivative term from the unitary transformation is found to be crucial in supplementing the transverse component of the electric field in higher orders. Final expressions are obtained for general combined electric and magnetic fields, including strong magnetic fields. The time derivative of the electric field is shown to enter only in the seventh order of the fine-structure constant if the transformation is carried out in the standard fashion. We put special emphasis on the case of strong fields, which are important for a number of applications, such as electrons bound in Penning traps.
Recommended Citation
A. Wienczek et al., "Foldy-Wouthuysen Transformation in Strong Magnetic Fields and Relativistic Corrections for Quantum Cyclotron Energy Levels," Physical Review A, vol. 106, no. 1, article no. 012816, American Physical Society, Jul 2022.
The definitive version is available at https://doi.org/10.1103/PhysRevA.106.012816
Department(s)
Physics
International Standard Serial Number (ISSN)
2469-9934; 2469-9926
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2023 American Physical Society, All rights reserved.
Publication Date
01 Jul 2022
Comments
John Templeton Foundation, Grant 60049570