  A self-consistent many-body approach is proposed to build a first-principles
crystal field theory, where crystal field parameters are calculated ab initio.
Many-body theory is used to write the energy of the interacting system as a
function of the density matrix of the noninteracting system. A variation of the
energy with respect to the density matrix gives an effective Hamiltonian that
is diagonalized to determine the density matrix providing the lowest energy.
The equations are written in terms of the Hopf algebra of functional
derivatives with respect to external fermionic sources. This approach contains
the many-body theory of Green functions as a special case, and the usual
crystal field theory as a first approximation. Therefore, it is expected to
provide good results for strongly-interacting electron systems.
