Abstract
We present a Bogolubov-Parasiuk-Hepp-Zimmermann formulation of the Weinberg renormalization scheme which leads to a graphwise infrared-convergent theory. Imposing the normalization conditions in the massless fermion theory and constraining suitably the mass dependence of the Green's functions leads to mass-independent coefficients in the Callan-Symanzik equation. It is shown for QED with a single fermion that this structure is compatible with gauge invariance.
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