Quantization of helicity on a compact spacetime

The Dirac operator arises naturally on from the connection on the Lie group U(1)×SU(2) and maps spacetime rays into rays in the Lie algebra. We construct both simple harmonic and pulse solutions to the neutrino equations on, classified by helicity and holonomy, using this map. Helicity is interpreted as the internal part of the Noether charge that arises from translation invariance; it is topologically quantized in integral multiples of a constant g that converts a Lie-algebra phase shift into an action. The fundamental unit of helicity is associated with a full twist in u(1)×su(2) phase per global lightlike cycle. If we pass to the projective space P¹xP³, we get half-integral helicity.