2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148757We present a particle-hole symmetric theory for a two-dimensional electron gas at filling factor one half. In this theory, elementary excitations are dipole-like fermions floating on top of the $ν=1/2$ boson quantum Hall liquid. In the absence of disorder these dipoles can form a Fermi-liquid. Disorder can break them apart and drive the ground state into a quantum critical state.An error in Eq.(11) is correctedMesoscale and Nanoscale Physicstext