W-INFINITY GAUGE THEORY AND THE QUANTUM HALL EFFECT

摘要

It is shown that a planar system of Hall electrons coupled to an applied electromagnetic field is written in the form of a W-infinity gauge theory. The W-infinity transformations mix Landau levels and the associated W-infinity gauge field consists of an infinite set of multipoles of the electromagnetic field. The W-infinity gauge theory provides a systematic way to classify the electromagnetic characteristics of the Hall system according to the resolution of external probes, and, in particular, offers an efficient means to construct the effective action by an algebraic procedure. Our approach is complementary to an earlier one and reveals a dual role the W-infinity gauge symmetry plays in the Hall dynamics. [References: 35]