Infrared problems in quantum electrodynamics: Reduction of coherent states and cross-section formulas

Dimensional-regularization techniques are used for the reduction of coherent states in quantum electrodynamics. The primary emphasis is on an unambiguous construction of the cross sections via a proper $S$-matrix theory. The proof of finiteness of the reduction formulas to all orders of perturbation theory proceeds formally on the basis of dimensional extensions of eikonal expressions for the Green's functions calculated on the mass shell. The method is illustrated by concrete second-order calculations in the particular examples of pair production and electron scattering in a potential. In the last example, some problems arising because of the "symmetric" definition of the $S$ matrix are discussed on a pragmatic basis.