Octonions and Fermions – Corinne A. Manogue

Date: Wed. April 14th, 2004, 2:30 pm-3:30 pm
Location: Rockefeller 221

Ten dimensional supersymmetric theories of physics such as superstring theory are at heart just higher dimensional generalizations of the Dirac equation. An enduring problem with these theories is how to reduce the spacetime dimension to the four we live in. I will describe a mechanism for reducing 10 spacetime dimensions to 4 without compactification, based on a generalization of the complex numbers known as the octonions. Applying this mechanism to the 10-dimensional Dirac equation leads to a treatment of both massive and massless particles on an equal footing. The resulting unified description has the correct particle spectrum to describe precisely 3 generations of leptons, with the correct number of spin/helicity states. In particular, the neutrinos naturally have only a single handedness. There is also a single sterile neutrino, a massless, spin-1/2 particle with the opposite helicity to the ordinary neutrinos and no generation structure.