Clifford Algebras, Pure Spinors and the Physics of Fermions

Abstract

The equations defining pure spinors are interpreted as equations of motion formulated on the lightcone of momentum space P = ℝ^{1, 9}. Most of the equations for fermion multiplets, usually adopted by particle physics, are then naturally obtained and their properties, such as internal symmetries, charges, and families, appear to be due to the correlation of the associated Clifford algebras with the three complex division algebras: complex numbers, quaternions and octonions. Pure spinors could be relevant not only because the underlying momentum space is compact, but also because they may throw some light on several problematic aspects of particle physics.