S-Matrix and Causality Condition. I. Maxwell Field

The general aim is to obtain maximum information about the $S$-matrix with a minimum of assumptions concerning the interaction. This program is carried through for the scattering of the electromagnetic field by a fixed center. The center is assumed spherically symmetric and of finite size, so that the causality condition can be applied. From this condition it follows rigorously that the $S$-matrix has a one-valued analytic continuation, whose only singularities are poles in the lower half-plane, and whose behavior at infinity can be specified. Particular consequences are: (i) the analytic properties of Wigner's function $R$; (ii) the integral relation connecting real and imaginary parts of $S$; (iii) relations connecting the sum of the oscillator strengths with the scattering cross section.