  The anomalous scaling in the Ginzburg-Landau model for the superconducting
phase transition is studied. It is argued that the negative sign of the $\eta$
exponent is a consequence of a special singular behavior in momentum space. The
negative sign of $\eta$ comes from the divergence of the critical correlation
function at finite distances. This behavior implies the existence of a Lifshitz
point in the phase diagram. The anomalous scaling of the vector potential is
also discussed. It is shown that the anomalous dimension of the vector
potential $\eta_A=4-d$ has important consequences for the critical dynamics in
superconductors. The frequency-dependent conductivity is shown to obey the
scaling $\sigma(\omega)\sim\xi^{z-2}$. The prediction $z\approx 3.7$ is
obtained from existing Monte Carlo data.
