Relativistic Electron Motion and Spin Precession

Abstract

The effects of spin precession and radiation on the motion of relativistic electrons are derived by employing a novel covariant treatment which is not based on the Dirac equation of relativistic quantum mechanics. By introducing the Lorentz-invariant universal time as the independent variable and by introducing a four-dimensional Lagrangian, which considers Coulomb, spin, and gravitation interactions, we extend the Hamilton–Jacobi formalism of classical mechanics from three to four dimensions. The resulting equations for the spin precession of the electron yield the BMT equations in the special case of homogeneous electromagnetic fields. The Stern–Gerlach experiment is discussed for nonpolarized electrons, and the Lorentz transformations are discussed within the frame of electron motion in Minkowski space.