Massive Relativistic Particle Model with Spin and Electric Charge from Two-Twistor Dynamics

Abstract

The sixteen real coordinates of two-twistor space are transformed by a nonlinear mapping into an enlarged space-time framework. The standard relativistic phase space of coordinates $(X_{\mu },P_{\mu })$ is supplemented by a six-parameter spin phase manifold (two pairs $({\eta }_{\alpha },{\sigma }_{\alpha })$ and $({\bar{\eta }}_{\dot{\alpha }},{\bar{\sigma }}_{\dot{\alpha }})$ of canonically conjugated Weyl spinors constrained by two second class constraints) and the electric charge phase space ($e,\varphi$). The free two-twistor classical mechanics is rewritten in this enlarged relativistic phase space as a model for a relativistic particle. Definite values for the mass, spin and the electric charge of the particle are introduced by means of three first class constraints.

LaTeX, 15 pages. A clarifying comment and a formula added. To appear in PLB

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