Dynamics of the relativistic electron spin in an electromagnetic field

Ritwik Mondal; Peter M Oppeneer

doi:10.1088/1361-648x/aba675

journal article Open Access Aug 17, 2020

Dynamics of the relativistic electron spin in an electromagnetic field

Ritwik Mondal

Peter M Oppeneer

Journal of Physics: Condensed Matter Vol. 32 No. 45 pp. 455802 · IOP Publishing

View at Publisher Save 10.1088/1361-648x/aba675

Abstract

Abstract
A relativistic spin operator cannot be uniquely defined within relativistic quantum mechanics. Previously, different proper relativistic spin operators have been proposed, such as spin operators of the Foldy–Wouthuysen and Pryce type, that both commute with the free-particle Dirac Hamiltonian and represent constants of motion. Here we consider the dynamics of a relativistic electron spin in an external electromagnetic field. We use two different Hamiltonians to derive the corresponding spin dynamics. These two are: (a) the Dirac Hamiltonian in the presence of an external field, and (b) the semirelativistic expansion of the same. Considering the Foldy–Wouthuysen and Pryce spin operators we show that these lead to different spin dynamics in an external electromagnetic field, which offers possibilities to distinguish their action. We find that the dynamics of both spin operators involve spin-dependent and spin-independent terms, however, the Foldy–Wouthuysen spin dynamics additionally accounts for the relativistic particle-antiparticle coupling. We conclude that the Pryce spin operator provides a suitable description of the relativistic spin dynamics in a weak-to-intermediate external field, whereas the Foldy–Wouthuysen spin operator is more suitable in the strong field regime.

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Details

Published: Aug 17, 2020
Vol/Issue: 32(45)
Pages: 455802
License: View

Authors

Funding

Vetenskapsrådet

Alexander von Humboldt-Stiftung

Knut och Alice Wallenbergs Stiftelse Award: 2015.0060

Universität Konstanz, Zukunftskolleg Award: P82963319

Cite This Article

Ritwik Mondal, Peter M Oppeneer (2020). Dynamics of the relativistic electron spin in an electromagnetic field. Journal of Physics: Condensed Matter, 32(45), 455802. https://doi.org/10.1088/1361-648x/aba675

Dynamics of the relativistic electron spin in an electromagnetic field

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