ON THE EQUIVALENCE OF RENORMALIZATIONS IN STANDARD AND DIMENSIONAL REGULARIZATIONS OF 2D 4-FERMION INTERACTIONS

We discuss the problem of equivalence between the standard (integer- d imensional d = 2) and the d = 2 + epsilon dimensional renormalization schemes for the complete U-N-symmetrical four-fermion interaction mode l. To ensure the multiplicative renormalizability of the theory, we ne ed three charges in the first case; in the second, we need an infinite series of independent charges g = {g(n), n = 0, 1,... }. After the us ual MS-renormalization. there exists a UV-finite renormalization of fi elds. Charges g --> g'(g) exist such that the renormalized Green's fun ctions in the limit epsilon --> 0 depend only on the three lower charg es g'(n)(g) with n = 0, 1,2. rather than on the whole set. This ensure s the possibility of establishing the equivalence of the two renormali zation schemes. The results of calculations in the MS scheme zip to tw o loops for the P-functions, and up to three loops for the anomalous f ield dimension gamma(psi) are presented. These are presented together with the derivation of the ''projection technique'' relations, which a llows one to express the higher renormalized composite operators of th e 4F-interaction via the lower ones in the limit epsilon --> 0.