The Dirac equation approach to spin-1/2 particle beam optics

The traditional approach to accelerator optics, based mainly on classical mechanics, is working excellently from the practical point of view. However, from the point of view of curiosity, as well as with a view to explore quantitatively the consequences of possible small quantum corrections to the classical theory, a quantum mechanical formalism of accelerator optics for the Dirac particle is being developed recently. Here, the essential features of such a quantum beam optical formalism for any spin-$\half$ particle are reviewed. It seems that the quantum corrections, particularly those due to the Heisenberg uncertainty, could be important in understanding the nonlinear dynamics of accelerator beams.