The contribution of effective quantum gravity to the high energy scattering in the framework of modified perturbation theory and one loop approximation

Abstract

The asymptotic behavior of the scattering amplitude for two scalar particles at high energies with fixed momentum transfers is studied. The study is done within the effective theory of quantum gravity based on quasi-potential equation. By using the modified perturbation theory, a systematic method is developed to find the leading eikonal scattering amplitudes together with corrections to them in the one-loop gravitational approximation. The relation is established and discussed between the solutions obtained by means of the operator and functional approaches applied to quasi-potential equation. The first non-leading corrections to the leading eikonal amplitude are found.

Functional Integral Method for Potential Scattering Amplitude in Quantum Mechanics

“…The eikonal approximation here is equivalent to the straight line approximation [6][7][8][9][10][11][12][13], which is used to compute the functional integrals as it occurs. The advantage of this approach is that, it can be extended to compute the leading term and the first-order correction term in the asymptotic scattering amplitude at Planck energies and the first-order correction in quantum linear gravity theory [14][15][16][17][18] and effective quantum gravity theory [19].…”