Quantum Mechanics on Phase Space
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This volume is the result of extensive research into the foundations of quantum mechanics, and presents a new formulation of quantum theory which resolves many existing problems. The formalism is experimentally motivated and is shown to be consistent with recent foundational approaches to quantum mechanics. It is based on new extensions of the theory of group representations, which are developed and illustrated in the text. This new approach establishes connections with quantum logic, philosophy, and the history of science, allowing a broad range of applications not only in physics, but also in such areas as signal processing and neuroscience. Audience: This book will be of interest to researchers and students. It is recommended as a supplementary textbook for advanced courses in quantum mechanics. A background in quantum mechanics and complex analysis is assumed. Booknews Offers a new mathematical formulation of quantum theory, clarifies a number of discrepancies within the prior formulation, describes new applications to experiments in physics, and extends the realm of application beyond physics to such fields as signal processing and neuroscience. The approach is based on new extensions of the theory of group representations, which are developed and illustrated in the text, and connects quantum theory with quantum logic, philosophy, and the history of science. Assumes a knowledge of basic topology and analysis, some modern abstract algebra, and at least rudimentary quantum mechanics. Annotation c. Book News, Inc., Portland, OR (booknews.com)
PrefaceCh. IBasic Quantum Theory and the Necessity for Its Revision11Classical Mechanics of Particles and Fluids12Structure of a Physical Model: State, Property (Observable) Measurement123Quantum Mechanics of a (Non-Relativistic Spinless) Particle184On the Connection between Classical Mechanics and Quantum Mechanics855Mathematical Appendix91Ch. IIBasic Experiments Suggest Generalizing Quantum Mechanics1341Quantum Mechanical Descriptions of an Experiment1352Capture on a Screen, in a Bubble Chamber, Gel, Cloud Chamber1413The Stern-Gerlach Experiment1584Crossed Polarizers1965Single Slit Experiments & Inapplicability of Heisenberg Uncertainty Relations2026Spontaneous Decay, Breit-Wigner (Cauchy) Distributions, and the Inapplicability of Heisenberg Type Uncertainty Relations2057Interferometers2078Imaging Processes and Signal Analysis2239Sensory Perception and Neuroscience24710Five Other Subjects and Their Implications25611Mathematical Appendix263Ch. IIIConstruction of Quantum Mechanics on Phase Space2901Group Representation Theory2922The Heisenberg Group (Weyl Algebra) and the Affine Group3903Representations of the Galilei Group4204Representations of the Poincare Group4435Remarks on the de Sitter Group510Ch. IVConsequences of Formulating Quantum Mechanics on Phase Space5131The Quantum/Classical Connection5132Quantum Field Theory5413Spring Cleaning in the House of Quantum Mechanics5584Reprise: Expanding the Realm of Application of Quantum Mechanics5655A Discrete (Lattice) Quantum Universe, and Computability565Ch. VFoundational Aspects5681Relation to Generalized Quantum Logic5682P.O.V.M.'s Arising on Operational Manuals5713Relation to Quantum Mechanical Measurement Theory6064Philosophical and Other Foundational Aspects613References627Index663
