EFFECTIVE-FIELD THEORY OF SINGLE AND MULTILAYERED QUANTUM HALL FLUIDS

We review an effective field theory of the quantum Hall fluid, where e lectron currents are expressed in terms of multiple-component gauge fi elds, and develop further the case of two-component fields. The form o f the effective action, a simple matrix Chern-Simons action, is dictat ed by the principles of current conservation, dimensional analysis, ga uge invariance, and by the presence of a gap. The formalism naturally describes multiple-component systems such as coupled Hall fluids in la yered geometries, in addition to describing more complicated single-fl uid states. We provide a complete classification of fractional quantum Hall states describable by two-component Chern-Simons gauge fields.