  Condensed matter systems undergoing second order transition away from the
critical fluctuation region are usually described sufficiently well by the mean
field approximation. The critical fluctuation region, determined by the
Ginzburg criterion, $\left \vert T/T_{c}-1\right \vert \ll Gi$, is narrow even
in high $T_{c}$ superconductors and has universal features well captured by the
renormalization group method. However recent experiments on magnetization,
conductivity and Nernst effect suggest that fluctuations effects are large in a
wider region both above and below $T_{c}$. In particular some "pseudogap"
phenomena and strong renormalization of the mean field critical temperature
$T_{mf}$ can be interpreted as strong fluctuations effects that are
nonperturbative (cannot be accounted for by "gaussian fluctuations"). The
physics in a broader region therefore requires more accurate approach. Self
consistent methods are generally "non - conserving" in the sense that the Ward
identities are not obeyed. This is especially detrimental in the symmetry
broken phase where, for example, Goldstone bosons become massive. Covariant
gaussian approximation remedies these problems. The Green's functions obey all
the Ward identities and describe the fluctuations much better. The results for
the order parameter correlator and magnetic penetration depth of the Ginzburg -
Landau model of superconductivity are compared with both Monte Carlo
simulations and experiments in high $T_{c}$ cuprates.
