According to the introduction it is the objective of the book to present an account of renormalized perturbation theory of models that have only one supersymmetry and are defined on flat 4-dimensional spacetime. Consequently supergravity and extended supersymmetries are not treated; also, even for simple supersymmetry possible phenomenological applications are not discussed. The scope of this treatise is best described in the authors’ own words: ”Our aim is the careful construction of higher orders in perturbation theory which permits a systematic search for anomalies”. The algebraic techniques that are used to establish the Ward identities avoid reference to any specific scheme of regularization and renormalization; this leads to an intrinsic formulation of the theories at hand based on symmetry principles, and yields an intrinsic definition of the anomalies that may break some of the postulated symmetries.
Chapter I is concerned with an introduction to supersymmetry algebra, superspace, superfields, and superconformal algebra, while Chapter II describes the tree approximation of all models that are analyzed subsequently, with special emphasis on Abelian and non-Abelian gauge models. In Chapter III perturbation theory in superspace is developed; this provides the basis for all higher order calculations, and allows for the construction of an action principle that is of crucial importance to the sequel. Chapter IV, entitled ”Renormalization: hard anomalies”, deals with the search for ultraviolet anomalies, and describes symmetry breaking by hard terms, it is shown that there is none for supersymmetry. The concluding Chapter V, entitled ”Renormalization: soft anomalies”, is concerned with infrared anomalies and related problems involving mass generation. A fairly extensive Appendix provides some very useful technical details.
This work is a textbook in the sense that it represents a systematic survey of a wealth of important material; it is also a research monograph in as much as it describes very recent results, including significant contributions due to the authors. The prerequisites are, however, quite demanding: it is clear from the outset that the reader is expected to have a thorough command of the background material, mathematical as well as physical. Be that as it may, the book is a most valuable addition to the literature.