A 2D spinless version of Dirac's equation written in a noninertial frame of reference

摘要

In this article, we present a quantized classical-like wave equation. It is obtained by considering the equivalence between the Hamilton-Jacobi eq. (which belongs to the usual manifold ?3 ? ? of General Relativity), with our two spinor versions of the Dirac eq. (which belongs to the associated complex manifold ? ? ?). In which the electron is considered as a particle-like entity, instead of the usual wave-like interpretation of standard Quantum Mechanics. We also consider the transformation properties between the two manifolds through the corresponding groups O(3,1) and SU(2), but we assume a flat Minkowsky space as the background space. We made an illustrative application to the rather standard problem of the hydrogen and helium atoms. We propose a variational extension of the approach, through a Hylleraas-like computational method, to take into account a many electron problem too futurely.