Solutions of the pion dispersion equation in the medium: new aspects

In symmetrical nuclear matter the solutions of pion dispersion equation are investigated in the complex plane of the pion frequency \omega. There are three well-known branches of solutions on the physical sheet : sound, pion and isobar, at the matter density less than the critical one \rho <\rho_c. At \rho >\rho_c the fourth branch appears on the physical sheet. For this branch the condition \omega^2_c\leq0 (in general case Re\omega^2_c\leq0) takes place. This points out the instability of the ground state which is possibly related to the pion condensation.