Theory of the fractional quantum Hall effect

A theory of the fractional quantum Hall effect is discussed. The generalised periodic boundary condition for a many-body system in a magnetic field is introduced. The ground state of the fractional quantum Hall system is degenerate. This degeneracy is determined by the denominator of the filling factor. Non-degenerate ground states produce the integral quantum Hall effect. The relation between the Hall conductance and the filling factor can be determined by conservation of the angular momentum.