  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.
