Distributional Celestial Amplitudes - Archive ouverte HAL
Article Dans Une Revue Journal of High Energy Physics Année : 2024

Distributional Celestial Amplitudes

Majdouline Borji
  • Fonction : Auteur

Résumé

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.

Dates et versions

hal-04426672 , version 1 (30-01-2024)

Identifiants

Citer

Yorgo Pano, Majdouline Borji. Distributional Celestial Amplitudes. Journal of High Energy Physics, 2024, 07, pp.120. ⟨10.1007/JHEP07(2024)120⟩. ⟨hal-04426672⟩
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