Foldy-Wouthuysen transformation for a Dirac-Pauli dyon and the Thomas-Bargmann-Michel-Telegdi equation

Abstract

The classical dynamics for a charged point particle with intrinsic spin is governed by a relativistic Hamiltonian for the orbital motion and by the Thomas-Bargmann-Michel-Telegdi equation for the precession of the spin. It is natural to ask whether the classical Hamiltonian (with both the orbital and spin parts) is consistent with that in the relativistic quantum theory for a spin-1/2 charged particle, which is described by the Dirac equation. In the low-energy limit, up to terms of the 7th order in $1/E_g$ ($E_g=2m{c}^2$ and $m$ is the particle mass), we investigate the Foldy-Wouthuysen (FW) transformation of the Dirac Hamiltonian in the presence of homogeneous and static electromagnetic fields and show that it is indeed in agreement with the classical Hamiltonian with the gyromagnetic ratio being equal to 2. Through electromagnetic duality, this result can be generalized for a spin-1/2 dyon, which has both electric and magnetic charges and thus possesses both intrinsic electric and magnetic dipole moments. Furthermore, the relativistic quantum theory for a spin-1/2 dyon with arbitrary values of the gyromagnetic and gyroelectric ratios can be described by the Dirac-Pauli equation, which is the Dirac equation with augmentation for the anomalous electric and anomalous magnetic dipole moments. The FW transformation of the Dirac-Pauli Hamiltonian is shown, up to the 7th order again, to be also in accord with the classical Hamiltonian.

18 pages

References in corpus (4)

• Foldy-Wouthyusen Transformation and Semiclassical Limit for Relativistic Particles in Strong External Fields
• Topological spin transport of relativistic electron
• Semiclassical Diagonalization of Quantum Hamiltonian and Equations of Motion with Berry Phase Corrections
• Semiclassical Dynamics of Dirac particles interacting with a Static Gravitational Field

Cited by in corpus (9)

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• Dunkl-Pauli Equation in the Presence of a Magnetic Field
• High-order Foldy-Wouthuysen transformations of the Dirac and Dirac-Pauli Hamiltonians in the weak-field limit
• Correspondence between classical and Dirac-Pauli spinors in view of the Foldy-Wouthuysen transformation
• Non-relativistic expansion of single-nucleon Dirac equation: Comparison between Foldy-Wouthuysen transformation and similarity renormalization group
• Non-relativistic expansion of Dirac equation with spherical scalar and vector potentials by reconstituted Foldy-Wouthuysen transformation
• Exact Foldy-Wouthuysen transformation of the Dirac-Pauli Hamiltonian in the weak-field limit by the method of direct perturbation theory
• Time-dependent Dunkl-Pauli Oscillator
• Maximum intrinsic spin-Hall conductivity in two-dimensional systems with k-linear spin-orbit interaction