The relativistic Schrödinger theory (RST) for N-fermion systems is further elaborated with respect to three fundamental problems which must emerge in any relativistic theory of quantum matter: (i) emergence/suppression of exchange forces between identical/non-identical particles, (ii) self-interactions, (iii) non-relativistic approximation. These questions are studied in detail for two-and three-particle systems but the results do apply to a general N-particle system. As a concrete demonstration, the singlet and triplet configurations of the positronium groundstate are considered within the RST framework, including a discussion of the corresponding hyperfine splitting.KEY WORDS: relativistic wave equations; solutions of wave equations; bound states; semiclassical theories and applications; matter waves.

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.

No abstract

No abstract

No abstract