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arXiv · 0704.2349

Quantum Master Equation for QED in Exact Renormalization Group

Yuji Igarashi·Katsumi Itoh·Hidenori Sonoda
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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.

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Yuji Igarashi, Katsumi Itoh, Hidenori Sonoda. 2007-04-18. Quantum Master Equation for QED in Exact Renormalization Group. https://doi.org/10.1143/ptp.118.121

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