The Spacetime Algebra provides an elegant language for studying the Dirac equation. We show how to perform cross section calculations following a method suggested by Hestenes (1982). The *S*-matrix is replaced with an operator which rotates the initial states into the scattered states. The method neatly handles spin dependence by allowing 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 neither are spin sums. Instead we deal with the spin orientation directly. We perform example calculations of spin dependence and polarization in Coulomb scattering to second order, and briefly consider more complicated calculations in QED.

A. Lewis, C.J.L. Doran and A.N. Lasenby, **Electron scattering without spin sums, ***Int. J. Theor. Phys.* **40**(1) (2001)