  Two-point functions related to the pion weak decay constant f_\pi are
calculated from the generating functional of chiral perturbation theory in the
mean-field approximation and the heavy-baryon limit. The aim is to demonstrate
that Lorentz invariance is violated in the presence of background matter. This
fact manifests itself in the splitting of both f_\pi and the pion mass into
uncorrelated time- and spacelike parts. We emphasize the different in-medium
renormalizations of the correlation functions, show the inequivalence between
the in-medium values of f_\pi deduced from Walecka-type models, on the one
hand, and QCD sum rules, on the other hand, and elaborate on the importance for
some nuclear physics observables.
