An Integer Basis for Celestial Amplitudes

TL;DR

This paper introduces a discrete basis of solutions for the massless Klein-Gordon equation in 3+1 Minkowski space, characterized by integer conformal dimensions and transformation properties, enabling a complete expansion of the Wightman function.

Contribution

It constructs a novel integer-dimension basis for massless fields in Minkowski space, facilitating new analytical tools for celestial amplitude analysis.

Findings

Basis elements form a complete set for the Klein-Gordon solutions.

Wightman function can be expressed as a quadratic sum over the basis.

Basis elements transform as conformal primaries and descendants.

Abstract

We present a discrete basis of solutions of the massless Klein-Gordon equation in 3+1 Minkowski space which transform as sl(2,C) Lorentz/conformal primaries and descendants, and whose elements all have integer conformal dimension. We show that the basis is complete in the sense that the Wightman function can be expressed as a quadratic sum over the basis elements.