Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.08877 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of 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.