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

References in corpus (4)

• The electronic properties of graphene
• Finite difference method for transport properties of massless Dirac fermions
• Single-cone real-space finite difference scheme for the time-dependent Dirac equation
• Fast and Exact Spin-s Spherical Harmonic Transforms

Cited by in corpus (10)

• Numerical solutions of Einstein's equations for cosmological spacetimes with spatial topology S3 and symmetry group U(1)
• The non-linear perturbation of a black hole by gravitational waves. II. Quasinormal modes and the compactification problem
• The numerical initial boundary value problem for the generalized conformal field equations
• Separability of test fields equations on the C-metric background
• Asymptotically flat vacuum initial data sets from a modified parabolic-hyperbolic formulation of the Einstein vacuum constraint equations
• Asymptotics of solutions of a hyperbolic formulation of the constraint equations
• Numerical construction of initial data sets of binary black hole type using a parabolic-hyperbolic formulation of the vacuum constraint equations
• Asymptotically hyperboloidal initial data sets from a parabolic-hyperbolic formulation of the Einstein vacuum constraints
• Criticality of inhomogeneous Nariai-like cosmological models
• Numerical initial data deformation exploiting a gluing construction: I. Exterior asymptotic Schwarzschild