A Fermion to Boson transformation is accomplished by attaching to each
Fermion a single flux quantum oriented opposite to the applied magnetic field.
When the mean field approximation is made in the Haldane spherical geometry,
the Fermion angular momentum lF is replaced by lB=lF−21(N−1).
The set of allowed total angular momentum multiplets is identical in the two
different pictures. The Fermion and Boson energy spectra in the presence of
many body interactions are identical if and only if the pseudopotential is
``harmonic'' in form. However, similar low energy bands of states with Laughlin
correlations occur in the two spectra if the interaction has short range. The
transformation is used to clarify the relation between Boson and Fermion
descriptions of the hierarchy of condensed fractional quantum Hall states.Comment: 5 pages, 4 figures, submitted to Physica
