The Spacetime Algebra provides an elegant language for studying the Dirac equation. Cross section calculations can be performed in an intuitive way following a method suggested by Hestenes. The S-matrix is replaced with an operator which rotates the initial states into the scattered states. We show how the method neatly handles spin dependence by allow ing the scattering operator to become a function of the initial spin. When the operator is independent of spin we can provide manifestly spin-independent results. Spin basis states are not needed, and we do no spin sums, instead dealing with the spin orientation directly. We perform some example calculations for single electron scattering and briefly discuss mor e complicated cases in QED.
A. Lewis, A.N. Lasenby and C.J.L. Doran, Electron scattering in the spacetime algebra, R. Ablamowicz and B. Fauser eds., 5th International Conference on Applications of Clifford Algebra, Ixtapa, Mexico 1999, 49-71 (2000)