Celestial Mellin amplitude

Celestial holography provides a promising avenue to studying bulk scattering in flat spacetime from the perspective of boundary celestial conformal field theory (CCFT). A key ingredient connecting two sides is amplitude, which given by Mellin transform momentum space amplitude energy. As such, amplitudes can be identified with correlation functions theory. In this paper, we introduce further notion coordinate. For technical reasons, focus on for scalar fields three dimensional dual 1D CCFT, and discuss block expansion. particular, poles encode scaling dimensions possible exchanged operators, while residues there are related OPE coefficient squares linear explicit way. We also compare obtained using inversion formulae. Finally, make some comments about generalizations higher dimensions.