Revisiting the compatibility problem between the gauge principle and the observability of the canonical orbital angular momentum in the Landau problem
Abstract
As is widelyknown, the eigenfunctions of the Landau problem in the symmetric gauge are specified by two quantum numbers. The first is the familiar Landau quantum number n, whereas the second is the magnetic quantum number m, which is the eigenvalue of the canonical orbital angular momentum (OAM) operator of the electron. The eigenenergies of the system depend only on the first quantum number n, and the second quantum number m does not correspond to any direct observables. This seems natural since the canonical OAM is generally believed to be a gaugevariant quantity, and observation of a gaugevariant quantity would contradict a fundamental principle of physics called the gauge principle. In recent researches, however, Bliokh et al. analyzed the motion of helical electron beam along the direction of a uniform magnetic field, which was mostly neglected in past analyses of the Landau states. Their analyses revealed highly nontrivial mdependent rotational dynamics of the Landau electron, but the problem is that their papers give an impression that the quantum number m in the Landau eigenstates corresponds to a genuine observable. This compatibility problem between the gauge principle and the observability of the quantum number m in the Landau eigenstates was attacked in our previous letter paper. In the present paper, we try to give more convincing answer to this delicate problem of physics, especially by paying attention not only to the particlelike aspect but also to the wavelike aspect of the Landau electron.
 Publication:

Annals of Physics
 Pub Date:
 November 2021
 DOI:
 10.1016/j.aop.2021.168647
 arXiv:
 arXiv:2104.10885
 Bibcode:
 2021AnPhy.43468647W
 Keywords:

 Landau problem;
 Electron helical beam;
 Canonical orbital angular momenta;
 Gauge principle and observability;
 Nucleon spin decomposition;
 Quantum Physics;
 High Energy Physics  Phenomenology;
 Nuclear Theory;
 Physics  Optics
 EPrint:
 Slightly compactified version to appear in Annals of Physics