Quantum Structures: A View of the Quantum World

We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their relations, are considered. Emphasis is placed on mutually global and irreducible structures. Is there a privileged structure of the closed system? Is there a preferred (bipartite) structure of an open system? Are there any practical advantages of certain alternative structures of the system? Is there a simple dynamical relation for a pair of structures? The [necessarily partial] answers are rather intriguing. Relativity of quantum correlations (that include entanglement as well as the "one-way" and "two-way" discord) is carefully presented. Emphasis is placed on the "parallel occurrence of decoherence" in the quantum Brownian motion. The environment-selected preferred structure of an open composite system is presented for a pair of harmonic oscillators (or the field modes). A limitation of the Nakajima-Zwanzig projection method appears as a consequence of quantum correlations relativity. Hence, describing dynamics of an alternate open-system is a delicate task. Certain interpretational issues, which include "quantum reference frames" issue, are discussed. Some recent experiments are also discussed. To this end, the option that "there are no particles" on the most fundamental physical level naturally follows. Certain open questions and prospects for further research are highlighted.