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Asymptotic behavior of the scattering amplitude for two scalar particles byscalar, vector and tensor exchanges at high energy and fixed momentum transfersis reconsidered in quantum field theory. In the framework of thequasi-potential approach and the modified perturbation theory a systematicscheme of finding the leading eikonal scattering amplitudes and its correctionsare developed and constructed. The connection between the solutions obtained byquasi-potential and functional approaches is also discussed. The firstcorrection to leading eikonal amplitude is found.

Planckian Scattering Beyond the Eikonal Approximation in the Quasi-potential Approach