Twistors, special relativity, conformal symmetry and minimal coupling - a review

TL;DR

This review explores a twistor-based approach to special relativity, constructing a model for a relativistic spinning charged particle with conformal symmetry, differing from traditional spin dynamics equations.

Contribution

It introduces a twistor and spinor framework for relativistic particle dynamics, emphasizing conformal invariance and minimal coupling, with a novel classical limit formulation.

Findings

Constructs a twistor-based model for spinning charged particles.

Derives a new classical limit of the Dirac operator in this framework.

Shows the resulting spin dynamics differ from the Thomas-Bargmann-Michel-Telegdi equation.

Abstract

An approach to special relativistic dynamics using the language of spinors and twistors is presented. Exploiting the natural conformally invariant symplectic structure of the twistor space, a model is constructed which describes a relativistic massive, spinning and charged particle, minimally coupled to an external electro-magnetic field. On the two-twistor phase space the relativistic Hamiltonian dynamics is generated by a Poincare scalar function obtained from the classical limit (appropriately defined by us) of the second order, to an external electro-magnetic field minimally coupled, Dirac operator. In the so defined relativistic classical limit there are no Grassman variables. Besides, the arising equation that describes dynamics of the relativistic spin differs significantly from the so called Thomas Bergman Michel Telegdi equation.