Michael Dütsch, Luis Peters, Karl-Henning Rehren
August 19, 2020
It is emphasized that for interactions with derivative couplings, the Ward Identity (WI) securing the preservation of a global gauge symmetry should be modified. Scalar QED is taken as an explicit example. More precisely, it is rigorously shown in scalar QED that the naive WI and the improved Ward Identity ("Master Ward Identity", MWI) are related to each other by a finite renormalization of the time-ordered product ("T-product") for the derivative fields; and we point out that the MWI has advantages over the naive WI - in particular with regard to the proof of the MWI. We show that the MWI can be fullfilled in all orders of perturbation theory by an appropriate renormalization of the T-product, without conflict with other standard renormalization conditions. Relations with other recent formulations of the MWI are established.