On the one-loop effective potential in quantum gravity

Physics

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Scientific paper

The one-loop effective potential is investigated in quantum gravity with or without cosmological constant in general D dimensions. It is shown that the partition function at the one-loop level depends only on the laplacian plus the scalar curvature with no terms of the form δ(0) ln g, i.e. Z(1-loop) = det-1/2 (Δ2 + 2R/D) × det1/2 (Δ1 + 2R/D). An explicit calculation is carried out at the one-loop level to demonstrate gauge independence of the partition function in a class of general linear gauges.

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