English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The classical dynamics for a charged spin particle is governed by the Lorentzforce equation for orbital motion and by the Thomas-Bargmann-Michel-Telegdi(T-BMT) equation for spin precession. In static and homogeneous electromagneticfields, it has been shown that the Foldy-Wouthuysen (FW) transform of theDirac-Pauli Hamiltonian, which describes the relativistic quantum theory for aspin-1/2 particle, is consistent with the classical Hamiltonian (with both theorbital and spin parts) up to the order of $1/m^{14}$ ($m$ is the particle'smass) in the low-energy/weak-field limit. In this paper, we extend thiscorrespondence to the case of inhomogeneous fields. Regardless of the fieldgradient (e.g., Stern-Gerlach) force, the T-BMT equation is unaltered and thusthe classical Hamiltonian remains the same, but subtleties arise and need to beclarified. For the relativistic quantum theory, we apply Eriksen's method toobtain the exact FW transformations for the two special cases, which inconjunction strongly suggest that, in the weak-field limit, the FW transformedDirac-Pauli Hamiltonian (except for the Darwin term) is in agreement with theclassical Hamiltonian in a manner that classical variables correspond toquantum operators via a specific Weyl ordering. Meanwhile, the Darwin term isshown to have no classical correspondence.

Correspondence between classical and Dirac-Pauli spinors in view of the Foldy-Wouthuysen transformation