Strong coupling Hartree-Fock approximation in the dynamical mean-field theory

In the limit of infinite spatial dimensions a thermodynamically consistent theory, which is valid for arbitrary value of the Coulombic interaction ($U<\infty$), is built for the Hubbard model when the total auxiliary single-site problem exactly splits into four subspaces with different ``vacuum states''. Some analytical results are given for the Hartree-Fock approximation when the 4-pole structure for Green's function is obtained: two poles describe contribution from the Fermi liquid component, which is ferromagnetic and dominant for small electron and hole concentrations (``overdoped case'' of high-$T_c$'s), whereas other two describe contribution from the non-Fermi liquid, which is antiferromagnetic and dominant close to half filling (``underdoped case'').