Igarashi, Yuji; Itoh, Katsumi; Sonoda, Hidenori Quantum master equation for QED in exact renormalization group. (English) Zbl 1131.81034 Prog. Theor. Phys. 118, No. 1, 121-134 (2007). 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 nilpotency of the BRS transformation is lost. 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. Cited in 3 Documents MSC: 81V10 Electromagnetic interaction; quantum electrodynamics 81V17 Gravitational interaction in quantum theory 81S25 Quantum stochastic calculus PDF BibTeX XML Cite \textit{Y. Igarashi} et al., Prog. Theor. Phys. 118, No. 1, 121--134 (2007; Zbl 1131.81034) Full Text: DOI arXiv