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

Abstract

Thus, at the present time there are two possible ways for instability to develop in gauge theories at high fermion density. In the four-dimensional Abelian model considered in [1] there is ultimately formed an anomalous state characterized by zero density of the real fermions, zero scalar condensate, and large gauge field condensate. In the two-dimensional model considered in the present paper, the effects of the complicated vacuum structure have the consequence that the system undergoes a transition to a normal state with low fermion density above a topologically nontrivial vacuum, this transition being accompanied by nonconservation of the fermion number. It is of undoubted interest to clarify which of these possibilities is realized in realistic non-Abelian four-dimensional theories (for example, in the standard model of electroweak interactions), i. e., to consider the existence of stable anomalous states in such theories. This question will be considered in later papers.