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

The asymptotic behavior of Planck energy elastic and inelastic amplitudes in quantum gravity is studied by means of the functional integration method. A straight-line path approximation is used to calculate the functional integrals which arise. Closed relativistically invariant expressions are obtained for the two “nucleons” elastic and inelastic amplitudes including the radiative corrections. Under the requirement of “softness” of the secondary gravitons a Poisson distribution for the number of particles emitted in the collision is found. Received: 6 December 1999 / Published online: 6 July 2000