QED and ortho-para- positronium mass difference

TL;DR

This paper investigates the mass difference between ortho- and para-positronium in relativistic QED using functional integral methods, revealing nonanalytic dependencies and limitations of relativistic QED in describing bound states.

Contribution

It demonstrates the importance of the nonphysical time variable and shows that relativistic QED cannot accurately describe real positronium bound states.

Findings

Nonphysical time variable significantly affects mass calculations.

Relativistic and non-relativistic QED yield different mass shift results.

Relativistic QED predicts abnormal 'time excitation' states.

Abstract

Bound state problem in the relativistic QED is investigated by the functional integral methods. The ortho- para- positron mass difference is calculated. Contribution of the "nonphysical"$~$ time variable turned out to be important and leads to the nonanalytic dependence of the bound state mass of the order $\alpha^{{2\over3}}$. It is shown that the relativistic and non-relativistic QED gives different results for this mass shift. In addition so-called abnormal states as "time excitations" arise. Sequential application of relativistic QED to bound state problem is in contradiction with real ortho- and para- positronium bound states. The conclusion: the relativistic QED is not suited to describe real bound states correctly.