Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 301 / 3 / iv / d / Solution

Average over the two initial electron spins and two initial photon polarizations, and sum over the final ones. The supplied fermion spin sum and photon polarization sum turn the result into gamma-matrix traces. The Clifford algebra impliesby anticommuting the outside matrix through the product. Together withthe two channel squares reduce, at $m=0$, to $-2e^{4}u/s$ and $-2e^{4}s/u$; the remaining cross terms cancel. Thus, in terms of the Mandelstam variables,Physical Compton kinematics has $s>0$ and $u<0$, so the displayed expression is nonnegative.