Translation of Harmonic Spinors and Interacting Weyl Fermions on Homogeneous Spaces

Abstract

We show that the image of the Poisson map, defined by Mehdi and Zierau in [MZ14b], which intertwines principal series representations with a submodule of the kernel of the cubic Dirac operator, commutes with the translation functor. As a byproduct, we obtain a systematic geometric process which produces interacting Weyl fermions with a fixed energy level on homogeneous spacetimes.In honor of Professor Jean LudwigIt is a first order Lorentz-invariant differential operator acting on sections of the spin bundle S over Minkowski spacetime. The spin bundle splits into half-spin bundles S + and S − so that