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

TL;DR

This paper introduces a spectral method for analyzing half-integer spin-weight functions on the sphere, demonstrating stability, convergence, and application to Dirac equation evolution on spherical manifolds.

Contribution

The paper develops a novel spectral scheme specifically for half-integer spin-weight functions and applies it to the Dirac equation on spherical geometries.

Findings

Stable and convergent spectral scheme for half-integer spin functions

Successful dynamical evolution of Dirac equation on spherical topology

Demonstration of the method's effectiveness for geometric PDEs

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.