Many-Particle Structure of Green’s Functions

Abstract

Since the reader may be unfamiliar with many-particle structure analysis (MPSA) of Green’s functions, I shall first present an introduction to this subject. The setting of MPSA is “axiomatic quantum field theory.” Axiomatic field theory, however, has many aspects; I will list, therefore, the various approaches, point out their distinctive features, and determine the relative position of MPSA. (The term “axioms” as used here merely denotes tentative postulates of a theory that it is hoped will describe elementary particle physics.) The following axioms common to all approaches (with one exception) are too well known to need discussion here (see, for example, Streater and Wightman, and Schweber1): I. Invariance under the inhomogeneous proper Lorentz group. II. Existence of local field operators. III. Mass spectrum conditions. IV. Completeness of the asymptotic particle states.