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Extension of the Shirafuji model for Massive Particles with Spin

S. Fedoruk·A. Frydryszak·J. Lukierski·C. Miquel-Espanya
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Abstract

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.

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S. Fedoruk, A. Frydryszak, J. Lukierski, C. Miquel-Espanya. 2005-10-31. Extension of the Shirafuji model for Massive Particles with Spin. https://doi.org/10.1142/s0217751x06031703

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