Twistor phase space dynamics and the Lorentz force equation

Abstract

Using the Lorentz force equation as an input a Hamiltonian mechanics on the nonprojective two twistor phase space T×T 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 T×T vanishes, the natural conformally invariant symplectic structure on T×T reduces to the natural symplectic structure on the cotangent bundle of the Kal/uża–Klein space.