Quantum Master Equation for QED in Exact Renormalization Group
High Energy Physics - Theory
2008-11-26 v1
Abstract
Recently, one of us (H.S.) gave an explicit form of the Ward-Takahashi identity for the Wilson action of QED. We first rederive the identity using a functional method. The identity makes it possible to realize the gauge symmetry even in the presence of a momentum cutoff. In the cutoff dependent realization, the abelian nature of the gauge symmetry is lost, breaking the nilpotency of the BRS transformation. Using the Batalin-Vilkovisky formalism, we extend the Wilson action by including the antifield contributions. Then, the Ward-Takahashi identity for the Wilson action is lifted to a quantum master equation, and the modified BRS transformation regains nilpotency. We also obtain a flow equation for the extended Wilson action.
Cite
@article{arxiv.0704.2349,
title = {Quantum Master Equation for QED in Exact Renormalization Group},
author = {Yuji Igarashi and Katsumi Itoh and Hidenori Sonoda},
journal= {arXiv preprint arXiv:0704.2349},
year = {2008}
}