  The problem of finding of the ferromagnetic and antiferromagnetic "symmetry
broken" solutions of the correlated lattice fermion models beyond the
mean-field approximation has been investigated. The calculation of the
quasiparticle excitation spectra with damping for the single- and multi-orbital
Hubbard model has been performed in the framework of the equation- of-motion
method for two-time temperature Green's Functions within a non-perturbative
approach. A unified scheme for the construction of Generalized Mean Fields
(elastic scattering corrections) and self-energy (inelastic scattering) in
terms of the Dyson equation has been generalized in order to include the
presence of the "source fields". The damping of quasiparticles, which reflects
the interaction of the single-particle and collective degrees of freedom has
been calculated. The "symmetry broken" dynamical solutions of the Hubbard
model, which correspond to various types of itinerant antiferromagnetism has
been discussed. This approach complements previous studies and clarifies the
nature of the concepts of itinerant antiferromagnetism and "spin-aligning
field" of correlated lattice fermions.
