Gauge-Invariant Energy Functional in Relativistic Schroedinger Theory

TL;DR

This paper develops a gauge-invariant energy functional within Relativistic Schroedinger Theory, analyzing positronium states and showing good agreement with conventional results under certain approximations.

Contribution

It introduces a gauge-invariant energy functional in RST that accounts for non-Abelian effects, improving upon previous non-invariant formulations.

Findings

Degeneracy of ortho- and para-positronium states depends on magnetic interactions and electric anisotropy.

Non-relativistic positronium spectrum in RST aligns well with conventional predictions.

Gauge invariance is achieved by considering non-Abelian characteristics of RST.

Abstract

The non-invariant energy functional of the preceding paper is improved in order to obtain its gauge-invariant form by strictly taking into account the non-Abelian character of Relativistic Schroedinger Theory (RST). As an application of the results, the dichotomy of positronium with respect to singlet and triplet states is discussed (ortho- and para-positronium). The degeneracy of the ortho- and para-states occurs in RST if (i) the magnetic interactions are neglected (as in the conventional theory) and (ii) the anisotropy of the electric interaction potential is disregarded. In view of such a very crude approximation procedure, the non-relativistic positronium spectrum in RST agrees amazingly well with the conventional predictions.