Distributional Celestial Amplitudes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866929212738240512 |
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| author | Pano, Yorgo Borji, Majdouline |
| author_facet | Pano, Yorgo Borji, Majdouline |
| contents | Scattering amplitudes are tempered distributions, which are defined through their action on functions in the Schwartz space $S(\mathbb{R})$ by duality. For massless particles, their conformal properties become manifest when considering their Mellin transform. Therefore we need to mathematically well-define the Mellin transform of distributions in the dual space $S'(\mathbb{R}^+)$. In this paper, we investigate this problem by characterizing the Mellin transform of the Schwartz space $S(\mathbb{R}^+)$. This allows us to rigorously define the Mellin transform of tempered distributions through a Parseval-type relation. Massless celestial amplitudes are then properly defined by taking the Mellin transform of elements in the topological dual of the Schwartz space $S(\mathbb{R}^+)$. We conclude the paper with applications to tree-level graviton celestial amplitudes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08877 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributional Celestial Amplitudes Pano, Yorgo Borji, Majdouline High Energy Physics - Theory Mathematical Physics Scattering amplitudes are tempered distributions, which are defined through their action on functions in the Schwartz space $S(\mathbb{R})$ by duality. For massless particles, their conformal properties become manifest when considering their Mellin transform. Therefore we need to mathematically well-define the Mellin transform of distributions in the dual space $S'(\mathbb{R}^+)$. In this paper, we investigate this problem by characterizing the Mellin transform of the Schwartz space $S(\mathbb{R}^+)$. This allows us to rigorously define the Mellin transform of tempered distributions through a Parseval-type relation. Massless celestial amplitudes are then properly defined by taking the Mellin transform of elements in the topological dual of the Schwartz space $S(\mathbb{R}^+)$. We conclude the paper with applications to tree-level graviton celestial amplitudes. |
| title | Distributional Celestial Amplitudes |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2401.08877 |