Lagrangian field theory in terms of green’s functions. I. Generalized perturbation theory and inversion theorems

Abstract

The problem of self-generating interactions in Lagrangian field theory is discussed in the Introduction which serves as a presentation for both papers on this subject. In this first paper we present a formal perturbation theory in terms of linked diagrams, about an arbitrary unperturbed system characterized by all its Green’s functions. Using this expansion, we present and prove a complete formulation of Lagrangian field theory in terms of Green’s functions. The parameters of the theory (potentials) are expressed in terms of the Green’s functions through Feynman diagrams. The results are interpreted in terms of a «dual» action operator, containing as potentials the connected Green’s functions. The relevance of this formulation to the problem of self-generating interactions is emphasized.