A formula for the static potential energy in quantum gravity

Details A formula for the static potential energy in quantum gravity A formula for the static potential energy in quantum gravity

1993-06-17

arxiv.org/abs/hep-th/9306078v2

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, LaTex, report CTP #2217, June 1993. -- REVISED VERSION: the section "Interaction energy versus ADM energy has been r

Scientific paper

We give a general expression for the static potential energy of the gravitational interaction of two massive particles, in terms of an invariant vacuum expectation value of the quantized gravitational field. This formula holds for functional integral formulations of euclidean quantum gravity, regularized to avoid conformal instability. It could be regarded as the analogue of the Wilson loop for gauge theories and allows in principle, through numerical simulations or other approximation techniques, non perturbative evaluations of the potential or of the effective coupling constant. The geometrical meaning of this expression is quite simple, as it represents the ``average proper-time delay'', respect to two neighboring lines, of a very long geodesic with unit timelike tangent vector.

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