  The behavior of the pion dispersion relation in a pion medium is strongly
modified by the introduction of a finite chemical potential associated to the
finite pion number density. Such behavior is particularly important during the
hadronic phase of a relativistic heavy-ion collision, between chemical and
thermal freeze-out, where the pion number changing processes, driven by the
strong interaction, can be considered to be frozen. We make use of an effective
Lagrangian that explicitly respects chiral symmetry through the enforcement of
the chiral Ward identities. The pion dispersion relation is computed through
the computation of the pion self-energy in a non-perturbative fashion by giving
an approximate solution to the Schwinger-Dyson equation for this self-energy.
Given the strong coupling between rho vectors and pions, we argue that the
modification of the pion mass due to finite pion density effects has to be
taken into account self-consistently for the description of the in-medium
modifications of rho's. We finally study some possible consequences of finite
pion density effects for the low-mass dilepton spectrum produced in
relativistic heavy-ion collisions.
