Abstract
Using the spacetime algebra formulation of the Dirac equation, we demonstrate how to perform cross-section calculations following a method suggested by Hestenes (1982). Instead of an S-matrix, we use an operator that rotates the initial states into the scattered states. By allowing the scattering operator to become a function of the initial spin, we can neatly handle spin-dependent calculations. When the operator is independent of spin, we can provide manifestly spin-independent results. We use neither spin basis nor spin sums, instead handling the spin orientation directly. As examples, we perform spin-dependent calculations in Coulomb scattering to second order, and briefly consider more complicated calculations in QED.
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Lewis, A., Doran, C. & Lasenby, A. Electron Scattering without Spin Sums. International Journal of Theoretical Physics 40, 363–376 (2001). https://doi.org/10.1023/A:1003716301776
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DOI: https://doi.org/10.1023/A:1003716301776