= Massive zero-momentum QED vertex integral
{title2=$\alpha=(D-2)^2/D,\ \beta=2-D$}
For the <QED> proper <Feynman vertex> with both external <four-momenta> zero, a massive internal <fermion> and a massless internal <photon> in <Feynman gauge>, the even numerator reduces under <Lorentz covariance> to $\gamma^\mu[\alpha k^2+\beta m^2]$. The <gamma matrices> identity $\gamma^\nu\gamma^\mu\gamma_\nu=(2-D)\gamma^\mu$ and the integrated replacement $k_\rho k_\sigma\mapsto g_{\rho\sigma}k^2/D$ prove the coefficients. The term $m^2/[k^2(k^2-m^2+i0)^2]$ has neither an <infrared divergence> nor an <ultraviolet divergence> for $m>0$; its integral in four dimensions is $-i/(16\pi^2)$. Only the remaining squared massive denominator supplies the <ultraviolet pole>.
Back to article page
