= Gordon identity
{c}
{title2=$2m\bar u\prime\gamma^a u$}
= Gordon decomposition
{c}
{synonym}
The <Gordon identity> rewrites a vector-current matrix element between equal-mass on-shell <Dirac spinors> using a momentum term and an antisymmetric spin term. In the mostly-minus convention $\{\Gamma^a,\Gamma^b\}=2\eta^{ab}$, $(\not p-m)u=0$, and $\Gamma^{ab}=[\Gamma^a,\Gamma^b]/2$, it reads $2m\bar u'\Gamma^au=\bar u'[(p'+p)^a-\Gamma^{ab}(p'_b-p_b)]u$. Derive it by adding the two external <Dirac equation> identities. The equivalent formula in the <mostly-plus Dirac convention> is $\bar u'[\gamma^{ab}(p'_b-p_b)+2m\gamma^a+p^a+p'^a]u=0$. The identity before division by $m$ remains valid for massless equal-mass states.
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