Regularization by higher derivatives and quantum correction for <Emphasis Type="Italic">N</Emphasis> = 1 supersymmetric theories

Some results of regularization by higher covariant derivatives used for investigation of the structure of quantum corrections in N = 1 supersymmetric theories are summarized in the present work. In particular, it is demonstrated that all integrals determining the Hell-Mann-Low functions in supersymmetric theories are integrals of total derivatives. As a consequence, in the N = 1 supersymmetric theories there exists an identity for the Green’s functions which follows from none of the symmetry theories known thus far. The problem of obtaining the exact β-function by the methods of perturbation theory is discussed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 5–35, May, 2008.