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arXiv · 2306.01155

Algebraic Approach to Relativistic Landau Levels in the Symmetric Gauge

Ulrich D. Jentschura
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Abstract

We use an algebraic approach to the calculation of Landau levels for a uniform magnetic field in the symmetric gauge with a vector potential A = (1/2) (B x r), where B is assumed to be constant. The magnetron quantum number constitutes the degeneracy index. An overall complex phase of the wave function, given in terms of Laguerre polynomials, is a consequence of the algebraic structure. The relativistic generalization of the treatment leads to fully relativistic bispinor Landau levels in the symmetric gauge, in a representation which writes the relativistic states in terms of their nonrelativistic limit, and an algebraically accessible lower bispinor component. Negative-energy states and the massless limit are discussed. The relativistic states can be used for a number of applications, including the calculation of higher-order quantum electrodynamic binding corrections to the energies of quantum cyclotron levels.

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Ulrich D. Jentschura. 2023-06-01. Algebraic Approach to Relativistic Landau Levels in the Symmetric Gauge. https://doi.org/10.1103/physrevd.108.016016

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