3-LOOP CALCULATION OF THE ANOMALOUS FIELD DIMENSION IN THE FULL 4-FERMION U-N-SYMMETRICAL MODEL

We present a three-loop calculation for the contribution of the anomal ous dimension gamma(psi), in the RG function for the full UN-symmetric model using dimensional regularization with d=2+E. This model contain s an infinite number of independent four-fermion interactions and coup lings g(n). In the MS scheme, the three-loop contribution in gamma(psi ) depends on all of the charges. In the symmetric subtraction scheme f or epsilon=0, only the dependence on the three lower charges g(0,1.2)' remains. The results of a three-loop calculation of gamma(psi) for th e Thirring model and for the Gross-Neveu model are discussed; they see n to contradict the equivalence of all four-fermion interactions for d =2, N=1. It is shown that this equivalence appears only for the symmet ric subtraction scheme. The precise meaning of (2+epsilon)-expansions of the critical dimensions is discussed for when the multiplication re normalizability is absent in the Gross-Neveu model.