Planckian Scattering Beyond the Eikonal Approximation in the Functional Approach

TL;DR

This paper investigates corrections to the leading eikonal approximation in Planckian-energy scattering using a functional integral approach, revealing retardation effects and potential non-eikonal contributions at short distances.

Contribution

It introduces a method to calculate non-leading correction terms in the scattering amplitude within the functional approach, highlighting the emergence of retardation effects.

Findings

First-order corrections induce retardation effects.

Correction terms are singular at short distances.

Non-eikonal contributions may arise from these corrections.

Abstract

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.