Localization and exact current compensation in the quantum Hall effect

A field-theoretic formulation of a planar Hall-electron system with edges is presented and some fundamental aspects of the integer quantum Hall effect are studied with emphasis on clarifying general symmetry-based consequences of localization. It is shown, in particular, that the immobility of localized electron states and current compensation by extended electron states, both crucial for quantization of the Hall conductance, are derived through the operation of magnetic translation of localized electron states alone. They actually are consequences of gauge invariance and hold under general circumstances with both level mixing and electron edge states taken into account.