Quasiaverages, symmetry breaking and irreducible

The development and applications of the method of quasiaverages to quantum statistical physics and to quan-tum solid state theory and, in particular, to quantum theory of magnetism, were considered. It was shown that the role of symmetry (and the breaking of symmetries) in combination with the degeneracy of the system was reanalyzed and essentially clarified within the framework of the method of quasiaverages. The problem of finding the ferromagnetic, antiferromagnetic and superconducting “symmetry broken ” solutions of the corre-lated lattice fermion models was discussed within the irreducible Green functions method. A unified scheme for the construction of generalized mean fields (elastic scattering corrections) and self-energy (inelastic scat-tering) in terms of the equations of motion and Dyson equation was generalized in order to include the “source fields”. This approach complements previous studies of microscopic theory of antiferromagnetism and clari-fies the concepts of Neel sublattices for localized and itinerant antiferromagnetism and “spin-aligning fields ” of correlated lattice fermions. Key words: quantum statistical mechanics, Bogolyubov’s quasiaverages, broken symmetry, quantum protectorate, quantum theory of magnetism, microscopic theory of superconductivity PACS: 05.30.-d, 05.30.Fk, 74.20.-z, 75.10.-b 1