For the N = 1 supersymmetric massless electrodynamics, regularized by higher derivatives, we describe a method, by which one can try to prove the new identity for the Green functions, which was proposed earlier. Using this method we show that some contribution to the new identity are really 0. * not break supersymmetry, and, unlike the dimensional reduction [6], it is not inconsistent. Using the higher derivative regularization allows revealing an interesting feature of the quantum correction structure in supersymmetric theories, which was first noted in Ref.[3]: All integrals defining the Gell-Mann-Low function are integrals of total derivatives and can be easily calculated. A similar feature takes place in non-Abelian supersymmetric theories [7,8]. (The calculations were made with a version of the higher derivative regularization, breaking the BRST-invariance and supplemented by a special subtraction scheme, which guarantees fulfilling the Slavnov-Taylor identities [9].) This feature was partially explained in Refs. [10,11]. According to these papers, substituting solutions of the Slavnov-Taylor identities into the Schwinger-Dyson equations, it is possible to obtain the exact β-function if we suppose existence of a new identity for Green functions. The explicit calculations up to the four-loop approximation [12,7] confirm this identity. A way of proving the new identity was proposed in Ref. [13]. However, it was based on the analysis of Feynman rules instead of strict functional methods. Moreover, it works only for a restricted class of diagrams. Nevertheless, an idea proposed in [13] can be strictly realized. This is demonstrated in this paper. We will see that it is possible to give a functional formulation for most equations, presented in Ref. [13]. The purpose of this paper is proposing of the method, which can be used for a strict proving (or disproving) the new identity in the massless N = 1 supersymmetric electrodynamics. As we will see later, using this method, it is possible to show that some contributions to the new identity are 0.This paper is organized as follows.In Sec. 2 we collect basic information about the N = 1 supersymmetric electrodynamics. In Sec. 3 we remind, how it is possible to calculate its β-function exactly to all orders, and also present a functional formulation of the new identity for Green functions, writing it as equality to 0 of some composite operators correlator. Calculation of this correlator is described in Sec. 4. The results are briefly discussed in the Conclusion. Some technical details of the calculations are presented in the Appendix.
