From Micro To Macro Quantum Systems: A Unified Formalism With Superselection Rules And Its Applications

Numerous sections of the book can be studied (and are really worth studying) like a textbook and without the necessity of going through the rest of the volume . . . certainly, everyone who works through the book will be rewarded by an enhanced comprehension of orthodox quantum theory . . . there are many solid reasons for recommending this book to the whole community of physicists and mathematicians - from graduate students to researchers - interested in a fresh description of the microscopic and macroscopic quantum worlds. Mathematical Reviews Traditional quantum theory has a very rigid structure, making it difficult to accommodate new properties emerging from novel systems. This book presents a flexible and unified theory for physical systems, from micro and macro quantum to classical. This is achieved by incorporating superselection rules and maximal symmetric operators into the theory. The resulting theory is applicable to classical, microscopic quantum and non-orthodox mixed quantum systems of which macroscopic quantum systems are examples. A unified formalism also greatly facilitates the discussion of interactions between these systems. A scheme of quantization by parts is introduced, based on the mathematics of selfadjoint and maximal symmetric extensions of symmetric operators, to describe point interactions. The results are applied to treat superconducting quantum circuits in various configurations. This book also discusses various topics of interest such as the asymptotic treatment of quantum state preparation and quantum measurement, local observables and local values, Schrödinger's cat states in superconducting systems, and a path space formulation of quantum mechanics. This self-contained book is complete with a review of relevant geometric and operator theories, for example, vector fields and operators, symmetric operators and their maximal symmetric extensions, direct integrals of Hilbert spaces and operators.