The split of the Dirac Hamiltonian into precisely predictable energy components
The author defines two operators \(V^\sim\) and \(H_0^\sim\) which -- when added -- yield the Dirac operator of the Hydrogen atom. These two operators can be seen as approximate potential and kinetic energy (plus rest energy). But unlike the potential energy and the kinetic energy itself, these represent completely predictable observables in the sense of von Neumann. The author's main mathematical result is, the absence of singular continuous spectrum of \(V^\sim\): A unitary operator is given that relates the positive part of \(V^\sim\) with the unperturbed Coulomb potential. The negative part has discrete spectrum only. In addition the paper contains some speculative remarks about neutrinos.
scientific article; zbMATH DE number 2146269