Conformal Primary Basis for Dirac Spinors

We study solutions to the Dirac equation in Minkowski space $mathbb{R}^{1,d+1}$ that transform as $d$-dimensional conformal primary spinors under the Lorentz group $SO(1,d+1)$. Such solutions are parameterized by a point in $mathbb{R}^d$ and a conformal dimension $Delta$. The set of wavefunctions that belong to the principal continuous series, $Delta =rac{d}2 + i u$, with $ ugeq 0$ and $ u in mathbb{R}$ in the massive and massless cases, respectively, form a complete basis of delta-function normalizable solutions of the Dirac equation. In the massless case, the conformal primary wavefunctions are related to the wavefunctions in momentum space by a Mellin transform.