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→=12(B→xr→), 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.
Recommended Citation
U. D. Jentschura, "Algebraic Approach To Relativistic Landau Levels In The Symmetric Gauge," Physical Review D, vol. 108, no. 1, article no. 016016, American Physical Society, Jul 2023.
The definitive version is available at https://doi.org/10.1103/PhysRevD.108.016016
Department(s)
Physics
Publication Status
Open Access
International Standard Serial Number (ISSN)
2470-0029; 2470-0010
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2023 American Physical Society, All rights reserved.
Publication Date
01 Jul 2023
Comments
National Science Foundation, Grant PHY–2110294