Magnetic Dipole Moment in Relativistic Quantum Mechanics

Abstract

We investigate relativistic quantum mechanics (RQM) for particles with arbitrary magnetic moment. We compare two well known RQM models: a) Dirac equation supplemented with an incremental Pauli term (DP); b) Klein-Gordon equations with full Pauli EM dipole moment term (KGP). We compare exact solutions to the external field cases in the limit of weak and strong (critical) fields for: i) homogeneous magnetic field, and ii) the Coulomb $1/r$-potential. For i) we consider the Landau energies and the Landau states as a function of the gyromagnetic factor ($g$-factor). For ii) we investigate contribution to the Lamb shift and the fine structure splitting. For both we address the limit of strong binding and show that these two formulations grossly disagree. We discuss possible experiments capable of distinguishing between KGP and DP models in laboratory. We describe impact of our considerations in astrophysical context (magnetars). We introduce novel RQM models of magnetic moments which can be further explored.

arXiv comment17.5 pages, 5 figures, references and a few paragraphs added, version accepted for publication in EPJ-A

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Cited by in corpus (15)

• Thermodynamics of Neutrons in a Magnetic Field and its Implications for Neutron Stars
• A short survey of matter-antimatter evolution in the primordial universe
• Motion of classical charged particles with magnetic moment in external plane-wave electromagnetic fields
• Matter-antimatter origin of cosmic magnetism
• Particle production at a finite potential step: Transition from Euler-Heisenberg to Klein paradox
• Effects of Landau quantization on neutrino emission and absorption
• Study of QED singular properties for variable gyromagnetic ratio $g\simeq 2$
• A Cusp in QED at g=2
• Classical neutral point particle in linearly polarized EM plane wave field
• Dynamic fermion flavor mixing through transition dipole moments
• Fermions with Electric Dipole Moment in curved spacetime
• Zero-Point Energy Density at the Origin of the Vacuum Permittivity and Photon Propagation Time Fluctuation
• Short Note on Spin Magnetization in QGP
• Quarks to Cosmos: Particles and Plasma in Cosmological evolution
• Emergence of periodic in magnetic moment effective QED action