Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry

Two-component spinors are the basic ingredients for describing fermions in quantum field theory in 3 + 1 spacetime dimensions. We develop and review the techniques of the two-component spinor formalism and provide a complete set of Feynman rules for fermions using two-component spinor notation. These rules are suitable for practical calculations of cross-sections, decay rates, and radiative corrections in the Standard Model and its extensions, including supersymmetry, and many explicit examples are provided. The unified treatment presented in this review applies to massless Weyl fermions and massive Dirac and Majorana fermions. We exhibit the relation between the two-component spinor formalism and the more traditional four-component spinor formalism, and indicate their connections to the spinor helicity method and techniques for the computation of helicity amplitudes.