Spin substructure of space-time

Space-time is provided with an underlying SL(2,C) spin space with complex noncommutative spinor coordinatesC ^A which satisfy . It is shown that the orbital angular momentum operator has a realization in this space as a derivative operator which can take on half-integral spin values, and the graded Lie algebra which describes the structure of the spin space is discussed. The spin-space translations mix fermi and bose fields and produce space-time translations which are not nil-potent. A hermitean metric with a line element which is invariant under such localx-dependent translations is introduced.