Effective Fermion Models in Symmetry-Breaking Phase and Quantum Chromodynamics

In our lecture we discuss the fermion models with quasilocal interaction implemented by derivatives and a momentum cutoff as substitutes of QCD at low energies. They are investigated in the strong coupling regime when several coupling constants are matched to their critical values. It is found that around polycritical points there appear a number of resonances with the same quantum numbers. Respectively the particular change of enviroment caused by gluon condensate results in the mass splitting independent of the cutoff. Such models are supposed to be an essential ingredient in the description of quark matter at high baryon densities.