Straight-line path approximation for high energy elastic and inelastic scattering in quantum gravity

The asymptotic behavior of Planck energy elastic and inelastic amplitudes i n quantum gravity is studied by means of the functional integration method. A straight-line path approximation is used to calculate the functional int egrals which arise. Closed relativistically invariant expressions are obtai ned for the two "nucleons" elastic and inelastic amplitudes including the r adiative corrections. Under the requirement of "softness" of the secondary gravitons a Poisson distribution for the number of particles emitted in the collision is found.