Assumption that the phase of the Coulomb field is a dynamical degree of freedom, conjugate to the charge operator, leads to the consistent, Lorentz invariant field theory of photons at spatial infinity, which depends parametrically on the value of the fine structure constant. We confirm existence of the normalizable bound state in the spectrum of the first Casimir operator of the Lorentz group. The state exists only for e² < \pi indicating that e²= \pi is the singular point of the theory. We also show that the theory has an essential singularity at the origin of the complex e² plane.

PACS numbers: 11.30.Cp, 03.65.Fd, 03.70.+k