On the Green’s functions of quantized fields. I

The temporal development of quantized fields, in its particle aspect, is described by propagation functions, or Green’s functions. The construction of these functions for coupled fields is usually considered from the viewpoint of perturbation theory. Although the latter may be resorted to for detailed calculations, it is desirable to avoid founding the formal theory of the Green’s functions on the restricted basis provided by the assumption of expandability in powers of coupling constants. These notes are a preliminary account of a general theory of Green’s functions, in which the defining property is taken to be the representation of the fields of prescribed sources.