  We show that the correlations of electrons with a fixed energy in metals have
very anomalous time and space dependences. Due to soft modes that exist in any
Fermi liquid, combined with the incomplete screening of the Coulomb interaction
at finite frequencies, the correlations in 2-d systems grow with time as $t^2$.
In the presence of disorder, the spatial correlations grow as the distance
squared. Similar, but in general weaker, effects are present in 3-d systems and
in the absence of quenched disorder. We propose ways to experimentally measure
these anomalous correlations.
