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September 20, 2025Open Access

Worldline proof of eikonal exponentiation

YDYuchen DuChinese Academy of Sciences SASiddarth AjithUniversity of Virginia RRRavisankar RajagopalUniversity of Virginia

Key Points

The 2-body scattering amplitude factorizes at each loop order, leading to the exponentiation of the eikonal phase.
This proof is derived using the worldline formalism, which offers a first quantized approach to scattering calculations.
The results apply to scalar particles interacting both electromagnetically and gravitationally.
The work builds on previous studies by Mogull, Plefka, and Steinhoff, enhancing understanding of scattering theory.

Abstract

A bstract In this paper, working in eikonal approximation, we present a proof for the exponentiation of the 2-body eikonal phase to all orders in the eikonal expansion , for scalar particles interacting electromagnetically or gravitationally. The proof is based on the worldline formalism, which is an alternative, first quantized method to the standard QFT calculation of the scattering amplitude. We show that in the worldline formalism the 2-body scattering amplitude written in impact parameter space naturally factorizes at each loop order. This factorization is responsible for the exponentiation of the eikonal phase, a result which was anticipated in the work of Mogull, Plefka, and Steinhoff 1.

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