Spin substructure of space-time (Q5903394)

The author investigates a spin-structure on space-time, with complex noncommutative spin coordinates \(C^ A\), such that \(x^{\dot AB}=1/2\{C^{\dot A},C^ B\}\). The generators of the Lorentz group have a simple realization in this space as derivative operators. The angular momentum operator can take half-integral spin values. In this model of spin space, a hermitian metric with a line element which is invariant under local x-dependent translations is introduced. The paper discusses the graded Lie algebra which describes the structure of the spin space.