Fermion spin sum

For on-shell Dirac spinors in standard relativistic normalization,

\sum_{r} u_{r} (p) \overset{u}{ˉ}_{r} (p) = \neq p + m, \sum_{r} v_{r} (p) \overset{v}{ˉ}_{r} (p) = \neq p - m .

These completeness identities turn spin-summed squared amplitudes into gamma-matrix traces.

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