Nonconservation of the fermion number and the limiting density of fermionic matter (two-dimensional gauge model)

The two-dimensional axial electrodynamics of fermions and bosons is investigated. It is shown that normal fermionic matter is unstable at densities higher than a critical density. The anomalous state, in its turn, is unstable, and by virtue of the complicated structure of the vacuum it goes over to the normal state with zero (or low) fermion density. Thus, in this model the fermion density cannot, in principle, exceed a certain critical value.