Renormalization issues for a whole abelian model

Considering that nature acts as a group, a whole abelian model is being developed. Classically, new aspects were observed as fields collective behavior and fields interacting among themselves and with mass through a global Lorentz force. This work analyzes some quantic aspects. Perturbation theory means that we know about 1-PI graphs. In a previous work, we have studied the quantum action principle, power-counting, primitively divergent graphs, Ward-Takahashi identities. This work concerns the study of counterterms and physical perturbation theory. It introduces a whole renormalization programme which informations are obtained from the common gauge parameter which establishes the fields set. It derives relationships between renormalization constants and on perturbative persistence on one asslessness field in the {A_I} set. It also argues on finitude possibilities through a whole expansion for the graphs