Daily Archives: September 3, 2007

The Algebra of Orthogonal Spin-1/2 States

Everybody knows that the quantum states of spin-1/2 particles come in two and only two independent spin orientations, for example spin +z and spin -z (up and down). My snuark theory uses spin-1/2 calculations to compute the Koide mass formulas, so it is a little inconvenient that snuarks need to come in six independent quantum states, +x, -x, +y, -y, +z and -z.

Three snuarks (no two antiparallel) combine to make one chiral handed lepton, the other three combine to make another chiral handed lepton, but traveling in the opposite direction. One chiral handed lepton could be a left handed electron moving in the +u direction, the other would be a left handed electron moving in the -u direction. Thus the six snuark degrees of freedom get turned into two spin-1/2 degrees of freedom.
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