STRAIGHT-LINE PATH APPROXIMATION FOR STUDYING PLANCKIAN-ENERGY SCATTERING IN QUANTUM-GRAVITY

A method is proposed for constructing a scattering amplitude in quantu m gravity by means of functional integration. The straight-line path a pproximation is used to calculate the functional integrals required. T he closed analytic, relativistically invariant expressions are obtaine d for the two-particle elastic-scattering amplitudes. In the limit of high energies S --> infinity and for given momentum transfers this exp ression for scattering amplitude takes a Glauber representation with a n eikonal function depending on the energy. The connection between thi s representation for the potential scattering amplitude and the eikona l approximation in quantum field theory is discussed.