A proper-time cure for the conformal sickness in quantum gravity

Details A proper-time cure for the conformal sickness in quantum gravity A proper-time cure for the conformal sickness in quantum gravity

2001-03-22

arxiv.org/abs/hep-th/0103186v2

Nucl.Phys.B606:357-379,2001

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 1 postscript figure; version to appear in Nucl. Phys. B with an added reference and a comment

Scientific paper

10.1016/S0550-3213(01)00227-9

Starting from the space of Lorentzian metrics, we examine the full gravitational path integral in 3 and 4 space-time dimensions. Inspired by recent results obtained in a regularized, dynamically triangulated formulation of Lorentzian gravity, we gauge-fix to proper-time coordinates and perform a non-perturbative ``Wick rotation'' on the physical configuration space. Under certain assumptions about the behaviour of the partition function under renormalization, we find that the divergence due to the conformal modes of the metric is cancelled non-perturbatively by a Faddeev-Popov determinant contributing to the effective measure. We illustrate some of our claims by a 3d perturbative calculation.

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