New methods for the renormalization group

The class of renormalization procedures with mass-independent counterterms is considered. It is shown to be nonempty. All these procedures, of which 't Hooft and Weinberg have given particular examples, lead to equivalent renormalization-group equations, which can be solved at arbitrary momenta, unlike the equations in the Gell-Mann-Low and Callan-Symanzik methods. Dimensional regularization is used throughout, as needed for non-Abelian gauge theories. It is shown how Weinberg's method using an ultraviolet cutoff extends to one using dimensional regularization. Finally, some calculations in quantum electrodynamics are exhibited.