Asymptotic scale invariance in a massive Thirring model

Abstract

The absence of Callan-Symanzik coupling-constant renormalization in a massive Thirring model is demonstrated to all orders using normal product methods. The derivation depends crucially on the mildness of the “anomaly” of the axial-vector Ward identity in this model, as well as on the special relationship between vector and axial-vector currents in two-dimensional field theory. Application of power-counting arguments establishes the asymptotic scale invariance of the vertex functions when the mass m tends to zero with the normalization point μ either fixed (Gell-Mann-Low limit) or vanishing with m (Callan-Symanzik limit).