Quantum Master Equation for QED in Exact Renormalization Group

Details Quantum Master Equation for QED in Exact Renormalization Group Quantum Master Equation for QED in Exact Renormalization Group

2007-04-18

arxiv.org/abs/0704.2349v1

Prog.Theor.Phys.118:121-134,2007

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, no figure

Scientific paper

10.1143/PTP.118.121

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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