Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-02-07
Physics
High Energy Physics
High Energy Physics - Theory
12 pages, prepared for the Proceedings of the 22nd Max Born Symposium, 27-29 September 2006, Wroc{\l}aw, Poland
Scientific paper
We extend the Shirafuji model for massless particles with primary spacetime coordinates and composite four-momenta to a model for massive particles with spin and electric charge. The primary variables in the model are the spacetime 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 spacetime and four-momenta vectors are composite, and the standard particle model, where both spacetime and four-momenta vectors are elementary. We quantize the model and find explicitly the first-quantized wavefunctions describing relativistic particles with mass, spin and electric charge. The spacetime coordinates in the model are not commutative; this leads to a wavefunction that depends only on one covariant projection of the spacetime four-vector defining plane wave solutions.
Fedoruk Sergey
Frydryszak Andrzej
Lukierski Jerzy
Miquel-Espanya Cesar
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