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Scalar amplitudes from fiber bundle geometry

Mohammad Alminawi1,*, Ilaria Brivio2,1,†, and Joe Davighi3,‡

  • *Contact author: mohammad.alminawi@physik.uzh.ch
  • †Contact author: ilaria.brivio@unibo.it
  • ‡Contact author: joseph.davighi@cern.ch
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Phys. Rev. D 113, 076005 – Published 6 April, 2026

DOI: https://doi.org/10.1103/qxwr-1vs6

Abstract

We compute tree-level n-point scattering amplitudes in scalar field theories in terms of geometric invariants on a fiber bundle. All 0- and 2-derivative interactions are incorporated into a metric on this bundle. The on-shell amplitudes can be efficiently pieced together from covariant Feynman rules, and we present a general closed formula for obtaining the n-point amplitude in this way. The covariant Feynman rules themselves can be derived using a generalization of the normal coordinate expansion of the fiber bundle metric. We demonstrate the efficiency of this approach by computing the covariant Feynman rules up to n=10 points, from which one can obtain the full amplitudes using our general formula. The formalism offers a prototype for obtaining geometric amplitudes in theories with higher-derivative interactions, by passing from the fiber bundle to its jet bundles.

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Phys. Rev. D 113, 076005– Published 6 April, 2026
  • Received 30 October 2025
  • Accepted 19 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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