Polarization sum for a massive vector boson (${\sum }_{\lambda }{ϵ}_{\mu }(k,\lambda ){ϵ}_{\nu }^{\ast }(k,\lambda )=-g_{\mu \nu }+k_{\mu }{k}_{\nu }/m^2$)

For $m>0$, the three physical polarization vectors are transverse to $k$ and have norm $-1$ in metric $(+---)$. In the rest frame their sum is $\mathrm{diag}(0,1,1,1)$; Lorentz covariance then gives the displayed expression for $k^2=m^2$. This includes the longitudinal mode. It cannot be specialized to $m=0$ by setting its denominator to zero.