Twistor Phase Space Dynamics and the Lorentz Force Equation

TL;DR

This paper develops a Hamiltonian framework on twistor phase space based on the Lorentz force, capturing relativistic spin dynamics and revealing geometric structures related to conformal invariance and Kaluza-Klein spaces.

Contribution

It introduces a novel Hamiltonian mechanics formulation on twistor phase space that incorporates charge and spin dynamics in a relativistic setting.

Findings

Reproduces classical relativistic spin dynamics

Shows charge as a dynamical variable

Links symplectic structures to conformal invariance and Kaluza-Klein geometry

Abstract

Using Lorentz force equation as an input a Hamiltonian mechanics on the non-projective two twistor phase space TxT is formulated. Such a construction automatically reproduces dynamics of the intrinsic classical relativistic spin. The charge appears as a dynamical variable. It is also shown that if the classical relativistic spin function on TxT vanishes, the natural conformally invariant symplectic structure on TxT reduces to the natural symplectic structure on the cotangent bundle of the Kaluza-Klein space.