  While the diagonalization of a quadratic bosonic form can always be done
using a Bogoliubov transformation, the practical implementation for systems
with a large number of different bosons is a tedious analytical task. Here we
use the coupled cluster method (CCM) to exactly diagonalise such complicated
quadratic forms. This yields to a straightforward algorithm which can easily be
implemented using computer algebra even for a large number of different bosons.
We apply this method on a Heisenberg system with two interpenetrating square
lattice antiferromagnets, which is a model for the quasi 2D antiferromagnet
Ba_2Cu_3O_4Cl_2. Using a four-magnon spin wave approximation we get a
complicated Hamiltonian with four different bosons, which is treated with CCM.
Results are presented for magnetic ground state correlations.
