Notion of potential in quantum gravity

The problem of a consistent definition of the quantum corrected gravitational field is considered in the Framework of the S-matrix method. The 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 l/r(2) terms in the potential, which are of zero order in the Planck constant (h) over bar, are shown to be independent of the gauge parameter weighting the gauge condition in the action. However, the l/r(3) terms, proportional to (h) over bar. 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 fur the gauge dependence is briefly discussed.