ON CHARGED FERMIONS IN TWO DIMENSIONS

Abstract

The integer quantum Hall effect and associated magnetic phenomena are reconsidered in a two-dimensional system with a flat boundary. The electromagnetic properties of this system are governed by an effective Lagrangian which includes an induced Chern-Simons term. The effective Lagrangian is relevant for the description of fields which are slowly varying about a uniform magnetic background associated with a fermionic ground state in which a whole number of Landau levels is filled. It is singular for field values that correspond to partially filled levels. The underlying assumption of translation invariance of the fermionic ground state fails in the vicinity of boundaries where the effective field theory is essentially nonlocal. The width of the boundary layer and the current flowing in it are estimated.