EXTENSION OF THE SHIRAFUJI MODEL FOR MASSIVE PARTICLES WITH SPIN
We extend the Shirafuji model for massless particles with primary space–time coordinates and composite four-momenta to a model for massive particles with spin and electric charge. The primary variables in the model are the space–time four-vector, four scalars describing spin and charge degrees of freedom as well as a pair of Weyl spinors. The geometric description proposed in this paper provides an intermediate step between the free purely twistorial model in two-twistor space in which both space–time and four-momenta vectors are composite, and the standard particle model, where both space–time and four-momenta vectors are elementary. We quantize the model and find explicitly the first-quantized wave functions describing relativistic particles with mass, spin and electric charge. The space–time coordinates in the model are not commutative; this leads to a wave function that depends only on one covariant projection of the space–time four-vector (covariantized time coordinate) defining plane wave solutions.