2011/10/31 by Tomasz M. Rusin, W. Zawadzki, Wlodek Zawadzki
Mathematics · Physics and Astronomy · #Condensed matter physics #Dirac (video compression format) #Electron #Field (mathematics) #Locality #Magnetic field #Mathematics #Philosophy #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum electrodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #Theoretical physics #Topological Materials and Phenomena #quant-ph
paper · pdf · doi:10.1088/1751-8113/45/31/315301
published as J. Phys. A: Math. Theor. 45 315301 (2012) · 11 pages 3 figures
openalex publication_date 2012/07/18 · arxiv created 2012/08/18 · arxiv updated 2012/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate a non-locality of Moss–Okninski transformation (MOT) used to separate positive and negative energy states in the 3+1 Dirac equation for relativistic electrons in the presence of a magnetic field. Properties of functional kernels generated by the MOT are analyzed and kernel non-localities are characterized by calculating their second moments parallel and perpendicular to the magnetic field. Transformed functions are described and investigated by computing their variances. It is shown that the non-locality of the energy-separating transformation in the direction parallel to the magnetic field is characterized by the Compton wavelength λ c = ℏ/ mc . In the plane transverse to the magnetic field, the non-locality depends both on magnetic radius L = (ℏ/ eB ) 1/2 and λ c . The non-locality of MOT for the 2+1 Dirac equation is also considered.