The gyrofrequency of a charged particle in a constant electromagnetic field: Pt. 2

The gyration angle and gyrofrequency for a charged particle in constant electric and magnetic fields of arbitrary orientation are derived directly from the Lorentz group. This is a new result and is entirely distinct from what is usually taken to be the relativistic gyrofrequency. Our expression agrees with the standard form only for parallel fields. The relativistic interaction between the linear and rotational components of the motion generates terms in the Lorentz group which are akin to the Thomas precession correction and are not ordinarily computable in the standard treatments. This derivation is made possible by utilizing the Clifford algebra of differential forms of Kahler and the author