The Master Ward Identity for Scalar QED
Abstract
It is emphasized that for interactions with derivative couplings, the Ward Identity (WI) securing the preservation of a global U(1) 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 timeordered product ("Tproduct") 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 fulfilled in all orders of perturbation theory by an appropriate renormalization of the Tproduct, without conflict with other standard renormalization conditions. Relations with other recent formulations of the MWI are established.
 Publication:

Annales Henri Poincaré
 Pub Date:
 September 2021
 DOI:
 10.1007/s0002302101048x
 arXiv:
 arXiv:2008.08514
 Bibcode:
 2021AnHP...22.2893D
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 81T10;
 81T15
 EPrint:
 v2: 33 pages, more selfcontained presentation. v1: 28 pages