  Formulation of quantum Hall dynamics using von Neumann lattice of guiding
center coordinates is presented. A topological invariant expression of the Hall
conductance is given and a new mean field theory of the fractional Hall effect
based on flux condensation is proposed. Because our mean field Hamiltonian has
the same form as Hofstadter Hamiltonian, it is possible to understand
characteristic features of the fractional Hall effect from Hofstadter's
spectrum. Energy gap and other physical quantities are computed and are
compared with the experiments. A reasonable agreement is obtained.

Condensed Matter;High Energy Physics - Theory