Classical vs Quantum Eikonal Scattering and its Causal Structure

TL;DR

This paper analyzes the classical and quantum aspects of gravitational scattering at high energies, revealing the role of group contraction in eikonal exponentiation and exploring causality and positivity bounds.

Contribution

It demonstrates the connection between group contraction and eikonal exponentiation, extending the analysis to all orders and including quantum corrections in gravitational scattering.

Findings

Eikonal exponentiation linked to $SU(2) o ISO(2)$ contraction.

Quantum corrections can dominate over Post-Minkowskian effects.

Established positivity bounds related to causality and time delay.

Abstract

We study the eikonal scattering of two gravitationally interacting bodies, in the regime of large angular momentum and large center of mass energy. We show that eikonal exponentiation of the scattering phase matrix is a direct consequence of the group contraction $SU(2)\to ISO(2)$, from rotations to the isometries of the plane, in the large angular momentum limit. We extend it to all orders in the scattering angle, and for all masses and spins. The emergence of the classical limit is understood in terms of the continuous-spin representations admitted by $ISO(2)$. We further investigate the competing classical vs quantum corrections to the leading classical eikonal scattering, and find several interesting examples where quantum corrections are more important than Post-Minkowskian's. As a case of study, we analyse the scattering of a photon off a massless neutral scalar field, up to next-to-leading order in the Newton constant, and to leading order in the fine structure constant. We investigate the causal structure of the eikonal regime and establish an infinite set of non-linear positivity bounds, of which positivity of time delay is the simplest.