On the equivalence of renormalizations in standard and dimensional regularizations of 2D four-fermion interactions

Autor: Vasil'ev, A. N., Vyazovskii, M. I., Derkachev, S. Ed., Kivel', N. A.
Zdroj: Theoretical and Mathematical Physics; April 1996, Vol. 107 Issue: 1 p441-455, 15p
Abstrakt: We discuss the problem of equivalence between the standard (integer-dimensional d=2) and the d=2+ε dimensional renormalization schemes for the complete UN-symmetrical four-fermion interaction model. To ensure the multiplicative renormalizability of the theory, we need three charges in the first case; in the second, we need an infinite series of independent charges g ≡ {gn, n=0, 1, ...}. After the usual MS-renormalization. there exists a UV-finite renormalization of fields. Charges g→g'(g) exist such that the renormalized Green's functions in the limit ε→0 depend only on the three lower charges g'n(g) with n=0, 1, 2. rather than on the whole set. This ensures the possibility of establishing the equivalence of the two renormalization schemes. The results of calculations in the MS scheme up to two loops for the β-functions, and up to three loops for the anomalous field dimension γφ are presented. These are presented together with the derivation of the “projection technique” relations, which allows one to express the higher renormalized composite operators of the 4F-interaction via the lower ones in the limit ε→0.
Databáze: Supplemental Index
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