Some addition theorems for spin-weighted spherical harmonics

TL;DR

This paper extends addition theorems to spin-weighted spherical harmonics, involving sums over azimuthal quantum numbers and derivatives, generalizing scalar harmonic results for applications in physics.

Contribution

It introduces new addition theorems for spin-weighted spherical harmonics, broadening the mathematical tools available for analyzing spin-weighted functions on the sphere.

Findings

Derived addition theorems involving derivatives of spin-weighted harmonics

Generalized scalar harmonic addition theorems to spin-weighted cases

Provides formulas useful for theoretical physics applications

Abstract

We present some addition theorems for spin-weighted spherical harmonics, generalizing previous results for scalar (spin-zero) spherical harmonics. These addition theorems involve sums over the azimuthal quantum number of products of two spin-weighted spherical harmonics at different points on the two-sphere, either (or both) of which are differentiated with respect to one of their arguments.