Planckian Scattering Beyond the Eikonal Approximation in the Functional   Approach
  In the framework of functional integration the non-leading terms to leading eikonal behavior of the Planckian-energy scattering amplitude are calculated by the straight-line path approximation. We show that the allowance for the first-order correction terms leads to the appearance of retardation effect. The singular character of the correction terms at short distances is also noted, and they may be lead ultimately to the appearance of non-eikonal contributions to the scattering amplitudes. 
Nguyen Suan Han and Nguyen Nhu Xuan