# The Master Ward Identity for scalar QED

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.

Keywords:

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