On The Quantum Theory of Hall Effect

Abstract

We discuss a model of both classical and integer quantum Hall-effect which is based on a semi-classical Schroedinger-Chern-Simons-action, where the Ohm-equations result as equations of motion. The quantization of the classical Chern-Simons-part of action under typical quantum Hall conditions results in the quantized Hall conductivity. We show further that the classical Hall-effect is described by a theory which arises as the classical limit of a theory of quantum Hall-effect. The model explains also the preference and the domain of the edge currents on the boundary of samples.