TY - JOUR
T1 - Magnetic dipole moment in relativistic quantum mechanics
AU - Steinmetz, Andrew
AU - Formanek, Martin
AU - Rafelski, Johann
N1 - Funding Information:
One of us (JR) thanks his colleagues Tobias Fischer and Lud-wik Turko at the University of Wroclaw for fruitful discussions, and acknowledges support of his visits in Wroclaw by the Polish National Science Center under contract No. UMO-2016/23/B/ST2/00720.
Publisher Copyright:
© 2019, Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/3/1
Y1 - 2019/3/1
N2 - 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 the impact of our considerations in the astrophysical context (magnetars). We introduce novel RQM models of magnetic moments which can be further explored.
AB - 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 the impact of our considerations in the astrophysical context (magnetars). We introduce novel RQM models of magnetic moments which can be further explored.
UR - http://www.scopus.com/inward/record.url?scp=85063333004&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85063333004&partnerID=8YFLogxK
U2 - 10.1140/epja/i2019-12715-5
DO - 10.1140/epja/i2019-12715-5
M3 - Article
AN - SCOPUS:85063333004
VL - 55
JO - European Physical Journal A
JF - European Physical Journal A
SN - 1434-6001
IS - 3
M1 - 40
ER -