On the notion of potential in quantum gravity

Details On the notion of potential in quantum gravity On the notion of potential in quantum gravity

2000-09-27

arxiv.org/abs/hep-th/0009220v1

Phys.Rev.D63:044004,2001

Physics

High Energy Physics

High Energy Physics - Theory

LaTex 2.09, 16 pages, 5 ps figures

Scientific paper

10.1103/PhysRevD.63.044004

The problem of consistent definition of the quantum corrected gravitational field is considered in the framework of the $S$-matrix method. Gauge dependence of the one-particle-reducible part of the two-scalar-particle scattering amplitude, with the help of which the potential is usually defined, is investigated at the one-loop approximation. The $1/r^2$-terms in the potential, which are of zero order in the Planck constant $\hbar,$ are shown to be independent of the gauge parameter weighting the gauge condition in the action. However, the $1/r^3$-terms, proportional to $\hbar,$ describing the first proper quantum correction, are proved to be gauge-dependent. With the help of the Slavnov identities, their dependence on the weighting parameter is calculated explicitly. The reason the gauge dependence originates from is briefly discussed.

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