Bogoliubov's Vision: Quasiaverages and Broken Symmetry to Quantum Protectorate and Emergence

TL;DR

This paper reviews the interconnected roles of symmetry principles, quasiaverages, and emergent phenomena like quantum protectorates in quantum and statistical physics, highlighting their conceptual unity and applications.

Contribution

It elucidates the relationships among symmetry breaking, quasiaverages, and quantum protectorates, emphasizing their unified role in many-body physics and complex systems.

Findings

Clarified the connection between quasiaverages and symmetry breaking.

Demonstrated the relevance of these concepts in magnetism and superconductivity.

Discussed applications to complex materials and molecular chirality.

Abstract

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.