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We study the behavior of the pion dispersion relation in a pion medium atfinite density and temperature. We introduce a pion chemical potential todescribe the finite pion number density and argue that such description isvalid during the hadronic phase of a relativistic heavy-ion collision betweenchemical and thermal freeze-out. We make use of an effective Lagrangian thatexplicitly respects chiral symmetry through the enforcement of the chiral Wardidentities. The pion dispersion relation is computed through the computation ofthe pion self-energy in a non-perturbative fashion by giving an approximatesolution to the Schwinger-Dyson equation for this self-energy. The dispersionrelation is described in terms of a density and temperature dependent mass andan index of refraction which is also temperature, density as well as momentumdependent. The index of refraction is larger than unity for all values of themomentum for finite $\mu$ and $T$. We conclude by exploring some of thepossible consequences for the propagation of pions through the boundary betweenthe medium and vacuum.Comment: 7 pages, 5 figures, 3 new references, published versio

Pion dispersion relation at finite density and temperature