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<p>In this paper, working in eikonal approximation, we present a proof for the exponentiation of the 2-body eikonal phase to <i>all orders in the eikonal expansion</i>, 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].</p>

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Worldline proof of eikonal exponentiation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月19日

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  • Yuchen Du,
  • Siddarth Ajith,
  • Ravisankar Rajagopal,
  • Diana Vaman

摘要

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].