Eikonal methods in classical bound-state problems and intense-field electrodynamics

A systematic treatment of bound-state problems is presented, using the hydrogen spectrum as a guide. The well-known binding energies are identified as poles of a subclass of Feynman diagrams, after eikonalization and the infinite-mass limit have been performed on the heavier of the two particles. Furthermore, the problem of an electron in a prescribed intense monochromatic field is studied with eikonal methods. The Green's function is examined in detail for the particular case of a scalar electron, and finally related to a spinor electron in a plane-wave field. Schwinger's functional methods are employed throughout.