Massive Particle Model with Spin from a Hybrid (spacetime-twistorial) Phase Space Geometry and Its Quantization

Fedoruk, Sergey; Frydryszak, Andrzej; Lukierski, Jerzy; Miquel-Espanya, Cèsar

Massive Particle Model with Spin from a Hybrid (spacetime-twistorial) Phase Space Geometry and Its Quantization

Authors

Fedoruk, Sergey

Frydryszak, Andrzej

Lukierski, Jerzy

Miquel-Espanya, Cèsar

Description

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.
12 pages, prepared for the Proceedings of the 22nd Max Born Symposium, 27-29 September 2006, Wrocław, Poland