The mathematical framework of Relativistic Schrödinger Theory (RST) is generalized in order to include the self-interactions of the particles as an integral part of the theory (i.e. in a non-perturbative way). The extended theory admits a Lagrangean formulation where the Noether theorems confirm the existence of the conservation laws for charge and energy-momentum which were originally deduced directly from the dynamical equations. The generalized RST dynamics is applied to the case of some heavy helium-like ions, ranging from germanium (Z = 32) to bismuth (Z = 83), in order to compute the interaction energy of the two electrons in their ground-state. The present inclusion of the electron self-energies into RST yields a better agreement of the theoretical predictions with the experimental data.

The characteristic features of ortho-and para-helium are investigated within the framework of Relativistic Schrödinger Theory (RST). The emphasis lies on the conceptual level, where the geometric and physical properties of both RST field configurations are inspected in detail. From the geometric point of view, the striking feature consists in the splitting of the u(2)-valued bundle connection A µ into an abelian electromagnetic part (organizing the electromagnetic interactions between the two electrons) and an exchange part, which is responsible for their exchange interactions. The electromagnetic interactions are mediated by the usual four-potentials A µ and thus are essentially the same for both types of field configurations, where naturally the electrostatic forces (described by the time component A 0 of A µ ) dominate their magnetostatic counterparts (described by the space part A of A µ ). Quite analogously to this, the exchange forces are as well described in terms of a certain vector potential (B µ ), again along the gauge principles of minimal coupling, so that also the exchange forces split up into an "electric" type ( B 0 ) and a "magnetic" type ( B). The physical difference of ortho-and para-helium is now that the first (ortho-) type is governed mainly by the "electric" kind of exchange forces and therefore is subject to a stronger influence of the exchange phenomenon; whereas the second (para-) type has vanishing "electric" exchange potential (B 0 ≡ 0) and therefore realizes exclusively the "magnetic" kind of interactions ( B), which, however, in general are smaller than their "electric" counterparts. The corresponding ortho/para splitting of the helium energy levels is inspected merely in the lowest order of approximation, where it coincides with the Hartree-Fock (HF) approximation. Thus RST may be conceived as a relativistic generalization of the HF approach where the fluid-dynamic character of RST implies many similarities with the density functional theory.KEY WORDS: relativistic wave equations; solutions of wave equations: bound states; semiclassical theories and applications.