Positive and Negative Mixtures in Relativistic Schrödinger Theory

Abstract

The general formalism of relativistic Schrodinger theory (RST) is specialized to a scalar two-particle system with electromagnetic interactions (scalar helium atom). The set of dynamically allowed field configurations splits up into positive and negative mixtures and pure states. The static and spherically symmetric solutions are constructed by means of first-order perturbation theory for the case of an attractive Coulomb potential. The corresponding energy levels for the positive and negative mixtures resemble the emergence of ortho and para states in the conventional quantum theory. The associated energy eigenvalues predicted by the RST seem to undergo a certain kind of mixture degeneracy as the RST analog of the conventional exchange degeneracy. The charge densities of the positive mixtures assimilate, whereas the densities of the negative mixtures recede from one another. Thus, positive (negative) mixtures strongly resemble the bosonic (fermionic) matter of the conventional theory when the Pauli principle is applied.