Polynomial reduction of a slashed vector
= Polynomial reduction of a slashed vector
{title2=$F(\not p)=A(p^2)\not p+B(p^2)I$}
The <Clifford algebra> gives $(\not p)^2=p^2I$. Splitting a scalar-coefficient <polynomial> into even and odd powers proves the displayed reduction. For an on-shell <fermion spin sum> assumed to be such a <polynomial>, $(\not p-m)P=0$ implies $P=A(\not p+m)$; the normalization $\operatorname{tr}(P\gamma^0)=4p^0$ fixes $A=1$ in four spacetime dimensions.