The density corrections, in terms of the isospin chemical potential ${\mu }_I,$ to the mass of the pions are studied in the framework of the $\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}$ low-energy effective chiral Lagrangian. The pion decay constant $f_{\pi }(T,{\mu }_I)$ is also analyzed. As a function of temperature for ${\mu }_I=0,$ the mass remains quite stable, starting to grow for very high values of T, confirming previous results. However, there are interesting corrections to the mass when both effects (temperature and chemical potential) are simultaneously present. At zero temperature the ${\pi }^{\pm }$ should condensate when ${\mu }_I=\mp m_{\pi }.$ This is no longer valid at finite T. The mass of ${\pi }_0$ acquires also a nontrivial dependence on ${\mu }_I$ due to the finite temperature.

• Received 27 December 2002

DOI:https://doi.org/10.1103/PhysRevD.67.074034