  In the present interdisciplinary review we focus on the applications of the
symmetry principles to quantum and statistical physics in connection with some
other branches of science. The profound and innovative idea of quasiaverages
formulated by N.N. Bogoliubov, gives the so-called macro-objectivation of the
degeneracy in domain of quantum statistical mechanics, quantum field theory and
in the quantum physics in general. We discuss the complementary unifying ideas
of modern physics, namely: spontaneous symmetry breaking, quantum protectorate
and emergence. The interrelation of the concepts of symmetry breaking,
quasiaverages and quantum protectorate was analyzed in the context of quantum
theory and statistical physics. The chief purposes of this paper were to
demonstrate the connection and interrelation of these conceptual advances of
the many-body physics and to try to show explicitly that those concepts, though
different in details, have a certain common features. Several problems in the
field of statistical physics of complex materials and systems (e.g. the
chirality of molecules) and the foundations of the microscopic theory of
magnetism and superconductivity were discussed in relation to these ideas.
