  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.
