  This paper reviews how a two-state, spin-one-half system transforms under
rotations. It then uses that knowledge to explain how momentum-zero,
spin-one-half annihilation and creation operators transform under rotations.
The paper then explains how a spin-one-half field transforms under rotations.
The momentum-zero spinors are found from the way spin-one-half systems
transform under rotations and from the Dirac equation. Once the momentum-zero
spinors are known, the Dirac equation immediately yields the spinors at finite
momentum. The paper then shows that with these spinors, a Dirac field
transforms appropriately under charge conjugation, parity, and time reversal.
  The paper also describes how a Dirac field may be decomposed either into two
4-component Majorana fields or into a 2-component left-handed field and a
2-component right-handed field. Wigner rotations and Weinberg's derivation of
the properties of spinors are also discussed.
