  Electromagnetic and gravitational central-field problems are studied with
relativistic quantum mechanics on curved space-time backgrounds. Corrections to
the transition current are identified. Analogies of the gravitational and
electromagnetic spectra suggest the definition of a gravitational
fine-structure constant. The electromagnetic and gravitational coupling
constants enter the Einstein-Hilbert-Maxwell Lagrangian. We postulate that the
variational principle holds with regard to a global dilation transformation of
the space-time coordinates. The variation suggests is consistent with a
functional relationship of the form alpha_QED being proportional to
alpha_G^(1/2), where alpha_QED is the electrodynamic fine-structure constant,
and alpha_G its gravitational analogue.
