2025/09/24 by Mohammad Alminawi, Ilaria Brivio, Alminawi, Mohammad +3 · 1 citation
Engineering · #FOS: Physical sciences #Geophysics and Sensor Technology #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.2509.20482
openalex publication_date 2025/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compute tree-level n-point scattering amplitudes in scalar field theories in terms of geometric invariants on a fibre 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 fibre 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 fibre bundle to its jet bundles.