$2$-Spinors via Linear Algebra

Abstract

We give a streamlined account of $2$-spinors, up to and including the Dirac equation, using little more than the resources of linear algebra. We prove that the Dirac bundle is isomorphic to the associated bundles ${\mathrm{SL}}_2(\mathbb{C}){\times }_{{\mathrm{SU}}_2}S$ and ${\mathrm{SL}}_2(\mathbb{C}){\times }_{{\mathrm{SU}}_2}\bar{S}$. A solution of the Dirac equation determines a pair of conjugate $2$-spinor fields over the mass shell $X_m$.

14 pages