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We discuss the algebra and the interpretation of the anomalous Zeeman effectand the spin-orbit coupling within the Dirac theory. Whereas the algebra forthe anomalous Zeeman effect is impeccable and therefore in excellent agreementwith experiment, the physical interpretation of that algebra uses images thatare based on macroscopic intuition but do not correspond to the meaning of thisalgebra. The interpretation violates the Lorentz symmetry. We give analternative intuitive description of the meaning of this effect, which respectsthe symmetry and is exact. It can be summarized by stating that a magneticfield makes any charged particle spin. We show also that the traditionaldiscussion about magnetic monopoles confuses two issues, viz. the symmetry ofthe Maxwell equations and the quantization of charge. These two issues defineeach a different concept of magnetic monopole. They cannot be merged togetherinto a unique all-encompassing issue. We also generalize the minimalsubstitution for a charged particle, and provide some intuition for themagnetic vector potential. We finally explore the algebra of the spin-orbitcoupling, which turns out to be badly wrong. The traditional theory that isclaimed to reproduce the Thomas half is based on a number of errors. Anerror-free application of the Dirac theory cannot account for the Thomasprecession, because it only accounts for the instantaneous local boosts, notfor the rotational component of the Lorentz transformation. This runs contraryto established beliefs, but Thomas precession can be understood in terms of theBerry phase on a path through the velocity space of the Lorentz group manifold.These results clearly reveal the limitations of the prevailing workingphilosophy to "shut up and calculate".

On magnetic monopoles, the anomalous g-factor of the electron and the spin-orbit coupling in the Dirac theory