  The fractional quantum Hall effect has been considered as a puzzling quantum
many-body phenomenon that has yet to be fully explained. The plateau width and
excitation energy gap are particularly problematic. We report here that those
two are determined by degrees of multi-particle correlations among the skipping
electrons forming the edge current flowing in incompressible strips (ISs).
Consideration of the total angular momentum of correlated skipping electrons
and their images, which are introduced to eliminate the confining potential
within the IS, yields additional Zeeman energies that hierarchically split the
Landau levels (LLs) by correlation order. This level splitting produces all the
odd-denominator plateaus and explains the occurrence of fractional charges,
while the split distances representing the correlation strengths determine both
plateau widths and excitation energy gaps. With such a scheme, we explicitly
reproduce an experimental Hall resistivity curve for the lowest LL and reveal
the characteristics of the half-filling state.
