Addition theorems for spin spherical harmonics. II Results

Abstract

Based on the results of part I, we obtain the general form of the addition theorem for spin spherical harmonics and give explicit results in the cases involving one spin-$s^{\prime }$ and one spin-$s$ spherical harmonics with $s^{\prime },s=1/2$, 1, 3/2, and $|s^{\prime }-s|=0$, 1. We obtain also a fully general addition theorem for one scalar and one tensor spherical harmonic of arbitrary rank. A variety of bilocal sums of ordinary and spin spherical harmonics are given in explicit form, including a general explicit expression for bilocal spherical harmonics.