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 $(X_μ, P_μ)$ is supplemented by a six-parameter spin phase manifold (two pairs $(η_α,σ_α)$ and $(\barη_{\dotα}, \barσ_{\dotα})$ of canonically conjugated Weyl spinors constrained by two second class constraints) and the electric charge phase space ($e,ϕ$). 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.