Scalar Amplitudes from Fibre Bundle Geometry
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915511735943168 |
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| author | Alminawi, Mohammad Brivio, Ilaria Davighi, Joe |
| author_facet | Alminawi, Mohammad Brivio, Ilaria Davighi, Joe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20482 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scalar Amplitudes from Fibre Bundle Geometry Alminawi, Mohammad Brivio, Ilaria Davighi, Joe High Energy Physics - Theory High Energy Physics - Phenomenology 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. |
| title | Scalar Amplitudes from Fibre Bundle Geometry |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2509.20482 |