Foundations of Quantum Theory: From Classical Concepts to Operator Algebras (Fundamental Theories of Physics Book 188)

Main subject categories: • Quantum theory • Classical-quantum duality • Operator algebras on Hilbert space • C*-algebras • Mathematical physicsThe aim of this book is to analyze the foundations of quantum theory from the point of view of classical-quantum duality, using the mathematical formalism of operator algebras on Hilbert space (and, more generally, C*-algebras) that was originally created by von Neumann (followed by Gelfand and Naimark). In support of this analysis, but also as a matter of independent interest, the book covers many of the traditional topics one might expect to find in a treatise on the foundations of quantum mechanics, like pure and mixed states, observables, the Born rule and its relation to both single-case probabilities and long-run frequencies, Gleason's Theorem, the theory of symmetry (including Wigner's Theorem and its relatives, culminating in a recent theorem of Hamhalter's), Bell's Theorem(s) and the like, quantization theory, indistinguishable particle, large systems, spontaneous symmetry breaking, the measurement problem, and (intuitionistic) quantum logic. One also finds a few idiosyncratic themes, such as the Kadison–Singer Conjecture, topos theory (which naturally injects intuitionism into quantum logic), and an unusual emphasis on both conceptual and mathematical aspects of limits in physical theories.This book is Open Access under a CC BY licence. This book explores the environmental competitiveness of 133 countries around the world, presenting an index evaluation system to facilitate a comparative analysis of environmental competitiveness on a global scale. This is a new way to measure competitiveness in the light of the contradiction between world economic development and environmental protection. Global environmental competitiveness covers five aspects: the ecological environment, resources environment, environmental management, environmental impacts and environmental coordination. The authors use longitudinal study and horizontal analysis, combining qualitative and quantitative analysis methods so as to conduct an in-depth study of theoretical, empirical and methodological issues of global environmental competitiveness. The work is presented here in three main parts beginning with the theory, technical road-map and analytical approach used. The second part reports on the countries as evaluation objects, analyzing the development status of global environmental competitiveness as a whole and revealing the strengths and weaknesses of each country's environmental competitiveness. Basic paths and strategies to enhance the competitiveness level are presented. In the third part the reader will discover a sub-report and evaluation of the environmental competitiveness for 133 countries around the world, revealing the characteristics and relative differences of countries representing different levels of development, in order to provide an important decision-making reference to those considering environmental economic policies, especially those considering accelerating a green economic transformation and enhancing environmental competitiveness. This book will appeal to scholars and professionals with an interest in environmental issues and environmental competitiveness at a global level, as well as those with an interest in each of the 133 countries analyzed in this text, including environmental policy makers in those countries This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C\*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence. Front Matter....Pages i-xxxvi Front Matter....Pages 21-21 Classical physics on a finite phase space....Pages 23-38 Quantum mechanics on a finite-dimensional Hilbert space....Pages 39-81 Classical physics on a general phase space....Pages 83-101 Quantum physics on a general Hilbert space....Pages 103-123 Symmetry in quantum mechanics....Pages 125-188 Front Matter....Pages 189-189 Classical models of quantum mechanics....Pages 191-245 Limits: Small \(\hbar \) ....Pages 247-291 Limits: large N ....Pages 293-331 Symmetry in algebraic quantum theory....Pages 333-366 Spontaneous Symmetry Breaking....Pages 367-433 The measurement problem....Pages 435-457 Topos theory and quantum logic....Pages 459-494 Back Matter....Pages 495-881

Environmental Economics; Climate Change/Climate Change Impacts; Green Development; Environmental Competitiveness; Environmental Coordination; Economy Transformation; Environmental Carrying; Environmental Management