Perturbation Theory in Superspace

Abstract

In the axiomatic approach to perturbative quantum field theory (cf. for instance [R.12]) which we follow here one defines in one way or the other perturbative Green’s functions and shows then that they satisfy the required axioms—in particular those of relativistic co-variance, causality and unitarity—in the sense of perturbation theory. Perturbation is usually performed in powers of a coupling constant or in the powers of ħ which counts the number of loops of associated Feyman diagrams. When, as is often the case in supersymmetry, fields of canonical dimension zero are present, one expands also in the number of fields. If mass generation occurs, the expansion will be in √ħ in ħ- arising in a well-defined way from an ħ-expansion. All of these expansions are considered as formal ones, i.e. questions of convergence of the series considered are not answered, in fact, not even posed.