AbstractThe quantum dynamics of a correlated quasi‐twodimensional (q2d) electron system showing the Quantum Hall Effect has been investigated. Galilei transformations are discussed for the correct description of quantum mechanical states in crossed electric and magnetic fields. Our quantum liquid site model with quasibosons carrying electromagnetic flux quanta uses a spatio‐temporary varying configuration of sites {R(t)}. Due to the nontrivial topology of the system and the multiple degeneracy of its ground state non Abelean Berry phases appear in the adiabatic time evolution.The calculation of the effective action functional has been carried out on the basis of a path integral approach. It is shown that the Berry phases entering the Greens function produce a Chern‐Simons‐like topological action term. Our theory yields a quantized conductivity tensor and, thus, exibita Quantum Hall behaviour. In calculating the local density of states of the inhomogeneous quantum liquid one obtains a remarkable broadening of peaks and a reduction of their