Electrodynamics of a Quantum Hall Liquid

We study the effects of electromagnetic fluctuations on the ground state and elementary excitations of a quantum Hall liquid. For filling factor ν=1/k we find that (i) the quasihole charge 𝑒* and statistics angle θ have a correction given by Δ𝑒*=α2μe/ε𝑘3 and Δθ=πΔ𝑒*/e, where α is the fine-structure constant, -e is the electron charge, and ε and μ are the dielectric constant and the magnetic permeability of the host semiconductor, respectively; (ii) the quasihole charge-density profile decays as 1/𝑟3 at large distances; (iii) collective modes with ω𝑞>c‖q‖/ √με are damped; in particular, at q=0, the cyclotron mode acquires an intrinsic linewidth Δω𝑐 given by Δω𝑐/ω𝑐=(2α/k) √ε/μ ; (iv) the Girvin-MacDonald order-parameter correlation function decays as 𝑟−η⁡(𝑟) at large distances, where η(r)=(k/2) +(α/π) √μ/ε ln(r/ξ); (v) despite these effects, the Hall resistivity is unchanged by electromagnetic fluctuations.