Exact Foldy-Wouthuysen transformation of the Dirac-Pauli Hamiltonian in the weak-field limit by the method of direct perturbation theory

Dah-Wei Chiou and Tsung-Wei Chen

Phys. Rev. A 94, 052116 – Published 15 November 2016

Abstract

We apply the method of direct perturbation theory for the Foldy-Wouthuysen (FW) transformation upon the Dirac-Pauli Hamiltonian subject to external electromagnetic fields. The exact FW transformations exist and agree with those obtained by Eriksen's method for two special cases. In the weak-field limit of static and homogeneous electromagnetic fields, by mathematical induction on the orders of $1 / c$ in the power series, we rigorously prove the long-held speculation: the FW transformed Dirac-Pauli Hamiltonian is in full agreement with the classical counterpart, which is the sum of the orbital Hamiltonian for the Lorentz force equation and the spin Hamiltonian for the Thomas-Bargmann-Michel-Telegdi equation.

Received 29 September 2016

DOI:https://doi.org/10.1103/PhysRevA.94.052116

Physics Subject Headings (PhySH)

Quantum correlations, foundations & formalism Relativistic wave equations

Atomic, Molecular & OpticalGeneral Physics

Authors & Affiliations

Dah-Wei Chiou^1,2,* and Tsung-Wei Chen^3,†

¹Department of Physics, National Taiwan Normal University, Taipei 11677, Taiwan
²Department of Physics and Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan
³Department of Physics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan

^*dwchiou@gmail.com
^†twchen@mail.nsysu.edu.tw

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Issue

Vol. 94, Iss. 5 — November 2016

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