Abstract
A method is proposed for constructing a scattering amplitude in quantum gravity by means of functional integration. The straight-line path approximation is used to calculate the functional integrals required. The closed analytic, relativistically invariant expressions are obtained for the two-particle elastic-scattering amplitudes. In the limit of high energiess→∞ and for given momentum transfers this expression for scattering amplitude takes a Glauber representation with an eikonal function depending on the energy. The connection between this representation for the potential scattering amplitude and the eikonal approximation in quantum field theory is discussed.
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