Gravitational Interactions and Fine-Structure Constant
Abstract
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 alphaQED being proportional to alphaG(1/2), where alphaQED is the electrodynamic fine-structure constant, and alphaG its gravitational analogue.