Fock Spaces, Landau Operators and the Regular Solutions of time-harmonic Maxwell equations
arXiv:1011.4628 · doi:10.1088/1751-8113/44/13/135303
Abstract
We investigate the representations of the solutions to Maxwell's equations based on the combination of hypercomplex function-theoretical methods with quantum mechanical methods. Our approach provides us with a characterization for the solutions to the time-harmonic Maxwell system in terms of series expansions involving spherical harmonics resp. spherical monogenics. Also, a thorough investigation for the series representation of the solutions in terms of eigenfunctions of Landau operators that encode dimensional spinless electrons is given. This new insight should lead to important investigations in the study of regularity and hypo-ellipticity of the solutions to Schrödinger equations with natural applications in relativistic quantum mechanics concerning massive spinor fields.
Exposition improved; Some typos corrected; Accepted for publication in J.Phys.A (February 2011). http://www.mat.uc.pt/preprints/ps/p1047.pdf