Two-Twistor Space, Commuting Composite Minkowski Coordinates and Particle Dynamics

TL;DR

This paper develops a twistor-based geometric framework with commuting coordinates, breaking internal symmetry and describing a relativistic particle with mass, spin, and charge in an extended phase space.

Contribution

It introduces a modified twistor approach that yields commuting space-time coordinates and an 18-dimensional phase space for relativistic particles with internal degrees of freedom.

Findings

Broken SU(2) symmetry to U(1) in twistor system

Decomposition of phase space into relativistic, spin, and charge sectors

Formulation of a particle model with mass, spin, and charge in extended phase space

Abstract

We employ the modification of the basic Penrose formula in twistor theory, which allows to introduce commuting composite space-time coordinates. It appears that in the course of such modification the internal symmetry SU(2) of two-twistor system is broken to U(1). We consider the symplectic form on two-twistor space, permitting to interpret its 16 real components as a phase-space. After a suitable change of variables such a two-twistor phase space is split into three mutually commuting parts, describing respectively the standard relativistic phase space (8 degrees of freedom), the spin sector (6 degrees of freedom) and the canonical pair angle-charge describing the electric charge sector (2 degrees of freedom). We obtain a geometric framework providing a twistor-inspired 18-dimensional extended relativistic phase space $\mathcal{M}^{18}$. In such a space we propose the action only with first class constraints, describing the relativistic particle characterized by mass, spin and electric charge.