Dynamics of the relativistic electron spin in an electromagnetic field

Journal of Physics. Condensed Matter : an Institute of Physics Journal
Ritwik Mondal, Peter M Oppeneer

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 opera...Continue Reading

References

Aug 1, 1995·Physical Review. B, Condensed Matter·T KraftH Eschrig
Apr 28, 2009·Physical Review Letters·M C Hickey, J S Moodera
Feb 13, 2016·Journal of Physics. Condensed Matter : an Institute of Physics Journal·J-E Wegrowe, E Olive
Jan 24, 2017·Journal of Inequalities and Applications·Saiful R Mondal
Mar 25, 2017·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Ritwik MondalPeter M Oppeneer
May 18, 2018·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Ritwik MondalPeter M Oppeneer

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