Classical Effective Field Theory for Weak Ultra Relativistic Scattering

TL;DR

This paper develops a classical effective field theory for weak ultra relativistic scattering, capturing instantaneous transverse field propagation and localizing particle equations of motion at the passing instant, applicable to scalar, electromagnetic, and gravitational interactions.

Contribution

It introduces a novel classical effective field theory framework for ultra relativistic scattering, including power counting, subleading corrections, and a gravitational field decomposition.

Findings

Reproduces leading scattering angles for various fields

Computes subleading corrections and interaction duration

Provides a gravitational field decomposition with non-linear action

Abstract

Inspired by the problem of Planckian scattering we describe a classical effective field theory for weak ultra relativistic scattering in which field propagation is instantaneous and transverse and the particles' equations of motion localize to the instant of passing. An analogy with the non-relativistic (post-Newtonian) approximation is stressed. The small parameter is identified and power counting rules are established. The theory is applied to reproduce the leading scattering angle for either a scalar interaction field or electro-magnetic or gravitational; to compute some subleading corrections, including the interaction duration; and to allow for non-zero masses. For the gravitational case we present an appropriate decomposition of the gravitational field onto the transverse plane together with its whole non-linear action. On the way we touch upon the relation with the eikonal approximation, some evidence for censorship of quantum gravity, and an algebraic ring structure on 2d Minkowski spacetime.