ABSTRACT
The Schwinger–De Witt technique is a powerful method for studying the effective action in theories with external fields. This technique was first introduced by J. Schwinger and later formulated in a general-covariant manner by B.S. De Witt. The Schwinger– De Witt technique is known to be well adapted to calculations of divergences and anomalies in the framework of the background field method. This chapter describes a superspace extension of the Schwinger–De Witt technique and explores it for investigating the structure of effective action superfunctional, including the analysis of divergences, anomalies and so on, in simple locally supersymmetric theories in a curved super space. The Schwinger-De Witt technique is an ideal tool for the study of breaking local symmetries by quantum corrections. The chapter demonstrates its power by giving explicit calculations of the so-called conformal anomaly. One of the specific features of superspace, as compared to ordinary space–time, is that any on-shell supersymmetry representation admits, in general, several off-shell superfield realizations.
