  General guidelines for constructing a quantum theory of charged-particle beam
optics starting ab initio from the basic equations of quantum mechanics,
appropriate to the situation under study. In the context of spin-1/2 particles,
these guidelines are used starting with the Dirac equation. The spinor theory
just constructed is used to obtain the transfer maps for normal and skew
magnetic quadrupoles respectively. As expected the traditional transfer maps
get modified by the quantum contributions. The classical limit of the quantum
formalism presented, reproduces the well-known Lie algebraic formalism of
charged-particle beam optics.

Accelerator Physics;Optics;Quantum Physics