Formulation of Abelian gauge theories without regulators. II

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Abstract
A new method of renormalizing Abelian gauge theories without regulators is developed in this series of papers. In the present part infrared problems are avoided by modifying the Lagrangian such that all masses are nonvanishing. It is shown that conventional renormalization of the classical Lagrangian leads to anomalies of the current. A modified renormalization scheme is proposed and shown to imply the classical form of partial current conservation and the desired Ward identities. Differential vertex operations are studied which will be used in paper III of this series for carrying out the required zero-mass limits.