Conformal primary basis for Dirac spinors
Lorenzo Iacobacci, Wolfgang Mück
Abstract
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 parametrized by a point in ${\mathbb{R}}^{d}$ and a conformal dimension $\mathrm{\ensuremath{\Delta}}$. The set of wave functions that belong to the principal continuous series, $\mathrm{\ensuremath{\Delta}}=\frac{d}{2}+i\ensuremath{\nu}$, with $\ensuremath{\nu}\ensuremath{\ge}0$ and $\ensuremath{\nu}\ensuremath{\in}\mathbb{R}$ 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 wave functions are related to the wave functions in momentum space by a Mellin transform.