QED and ortho-para- positronium mass difference

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.