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The formulation of an exact functional renormalization group equation for Quantum Einstein Gravity necessitates that the underlying effective average action depends on two metrics, a dynamical metric giving the vacuum expectation value of the quantum field, and a background metric supplying the coarse graining scale.
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E. Manrique and M. Reuter, Annals Phys. 325
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J. E. Daum, U. Harst and M. Reuter, JHEP 01
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M. Shaposhnikov and C. Wetterich, Phys. Lett. B 683
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