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

TL;DR

This paper develops a classical relativistic particle model incorporating spin and electric charge by transforming two-twistor space coordinates into an extended phase space, with constraints setting particle properties.

Contribution

It introduces a novel two-twistor based framework that unifies spin and charge in a classical relativistic particle model using an enlarged phase space.

Findings

Model successfully encodes fixed mass, spin, and charge via constraints.

Provides a new geometric interpretation of particle properties in twistor space.

Extends twistor theory to include electric charge and spin variables.

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 ($e,\phi$). 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.