Ns. Han et E. Ponna, STRAIGHT-LINE PATH APPROXIMATION FOR STUDYING PLANCKIAN-ENERGY SCATTERING IN QUANTUM-GRAVITY, Nuovo cimento della Società Italiana di Fisica. A. Nuclei, particles and fields, 110(5), 1997, pp. 459-473
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.