Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-10-31
Int.J.Mod.Phys.A21:4137-4160,2006
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 27 pages, appendix.sty, newlfont.sty (attached)
Scientific paper
10.1142/S0217751X06031703
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 (covariantized time coordinate) defining plane wave solutions.
Fedoruk Sergey
Frydryszak Andrzej
Lukierski Jerzy
Miquel-Espanya Cesar
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