Precession of relativistic particles of arbitrary spin in a slowly varying electromagnetic field

It is shown that, under accelerator or bubble-chamber conditions, the passage of a particle of arbitrary spin through an electromagnetic field effects a Lorentz transformation on its momentum and polarization, and a linear differential equation determining this transformation is given. We also give explicitly the decay-time dependence of the angular distribution that describes the decay of a particle moving in an electromagnetic field, and thereby obtain a method, explained in detail, of measuring the magnetic moment of an unstable, higher spin particle like the Ω-. It is noted that the gyromagnetic ratio g=2 leads to particularly simple equations of motion for all spins, and not only for spin 1/2. In an appendix we use a novel covariant algebraic method to solve the equations of motion and obtain the finite Lorentz transformation, in the case of a constant and homogeneous electromagnetic field. The method involves the introduction of an algebra of 4-by-4 matrices that plays the same role for 4-vectors as the Dirac algebra for 4-spinors.