# Electrodynamics of a quantum Hall liquid

## Abstract

We study the effects of electromagnetic fluctuations on the ground state and elementary excitations of a quantum Hall liquid. For filling factor =1/k we find that (i) the quasihole charge e* and statistics angle have a correction given by e*=2e/k3 and =e*/e, where is the fine-structure constant, -e is the electron charge, and and 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 q>cq/ are damped; in particular, at q=0, the cyclotron mode acquires an intrinsic linewidth c given by c/c=(2/k) /; (iv) the Girvin-MacDonald order-parameter correlation function decays as r-(r) at large distances, where (r)=(k/2) +(/) /ln(r/); (v) despite these effects, the Hall resistivity is unchanged by electromagnetic fluctuations. © 1992 The American Physical Society.