  We present a mapping of elementary fermion operators onto a quadratic form of
composite fermionic and bosonic operators. The mapping is an exact isomorphism
as long as the physical constraint of one composite particle per cluster is
satisfied. This condition is treated on average in a composite particle
mean-field approach, which consists of an ansatz that decouples the composite
fermionic and bosonic sectors. The theory is tested on the one- and
two-dimensional Hubbard models. Using a Bogoliubov determinant for the
composite fermions and either a coherent or Bogoliubov state for the bosons, we
obtain a simple and accurate procedure for treating the Mott insulating phase
of the Hubbard model with mean-field computational cost.
