Algebraic Approach to Relativistic Landau Levels in the Symmetric Gauge

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.

7 pages; RevTeX

References in corpus (2)

• Landau Levels and the Issue of Gauge Invariance in Confined Spaces
• Foldy-Wouthuysen Transformation in Strong Magnetic Fields and Relativistic Corrections for Quantum Cyclotron Energy Levels

Cited by in corpus (6)

• Transmission of vortex electrons through a solenoid
• Emission of twisted photons by a scalar charged particle in a strong magnetic field
• Emission of twisted photons by a Dirac electron in a strong magnetic field
• Quantum Electrodynamic Corrections to Cyclotron States in a Penning Trap
• Eighth-Order Foldy-Wouthuysen Transformation
• Radiative Energy and Mass Shifts of Quantum Cyclotron States