A spectral method for half-integer spin fields based on spin-weighted spherical harmonics

Abstract

We present a new spectral scheme for analysing functions of half-integer spin-weight on the $2$-sphere and demonstrate the stability and convergence properties of our implementation. The dynamical evolution of the Dirac equation on a manifold with spatial topology of $\mathbb{S}^2$ via pseudo-spectral method is also demonstrated.

25 pages, 18 figures. Agrees with the published version