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

Journal Article · Thu Jul 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.012115· OSTI ID:21440466

Chen, Tsung-Wei ^[1]; Chiou, Dah-Wei ^[2]

---

1. Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 106, Taiwan (China)
2. Department of Physics, Beijing Normal University, Beijing 100875 (China)

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 seventh order in 1/E{sub g} (E{sub g}=2mc{sup 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 seventh-order again, to be in accord with the classical Hamiltonian as well.

• OSTI ID: 21440466
• Journal Information: Physical Review. A, Vol. 82, Issue 1; Other Information: DOI: 10.1103/PhysRevA.82.012115; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHARGED PARTICLES
DIRAC EQUATION
DUALITY
DYONS
ELECTROMAGNETIC FIELDS
FOLDY-WOUTHUYSEN TRANSFORM
GYROMAGNETIC RATIO
HAMILTONIANS
MAGNETIC DIPOLE MOMENTS
PRECESSION
QUANTUM FIELD THEORY
RELATIVISTIC RANGE
REST MASS
SPIN
ANGULAR MOMENTUM
CANONICAL TRANSFORMATIONS
DIFFERENTIAL EQUATIONS
DIPOLE MOMENTS
ELEMENTARY PARTICLES
ENERGY RANGE
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
MAGNETIC MOMENTS
MASS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
POSTULATED PARTICLES
QUANTUM OPERATORS
TRANSFORMATIONS
WAVE EQUATIONS