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We generalize the Laughlin argument for the integer quantum Hall effect ofnon-interacting two-dimensional electrons by taking into account the fullthree-dimensional nature of gauge symmetry. This naturally leads to theprediction of the principal experimental results on the quantum Hall effect,including the integer and fractional values and plateau widths of quantizedHall conductance. The approach includes, in a fundamental way, the influence ofspin, allowing the description of both single electrons and Cooper pairs. Notrequiring the introduction of strongly correlated multi-particle states nor akey role for disorder, the unified analysis sheds light on the profoundconnection between dimensionality, symmetry, and quantum behavior.

A unified non-interacting-electron theory of the integer and fractional quantum Hall conductance