Complete the interacting-edge action simplification for fractional quantum Hall case

Complete the analytical simplification of the edge-mode action S = ∫[Ψ* U† i ∂(UΨ) − Ψ* U† H′ U Ψ] (Equation (e24)) in the presence of interparticle interaction terms, accounting for two-point density correlations, to derive a tractable effective edge action for fractional quantum Hall systems under time-dependent magnetic fields.

Background

To describe edge dynamics, the authors construct a unitary deformation U = e^{-i ĤF} implementing area-preserving diffeomorphisms and derive an action involving the transformed Hamiltonian H′ that includes a confining potential and interaction terms. While star-product techniques simplify the non-interacting (integer) case, interaction terms introduce significant complications through two-point correlations.

Because of these complications, the authors defer completing the interacting calculation and confine their detailed analysis to the integer Hall effect. Finishing this calculation would enable a full fractional edge theory under time-dependent magnetic fields.