Mathematical Foundations of Quantum TheoryA.R. Marlow Mathematical Foundations of Quantum Theory is a collection of papers presented at the 1977 conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The contributors present their topics from a wide variety of backgrounds and specialization, but all shared a common interest in answering quantum issues. Organized into 20 chapters, this book's opening chapters establish a sound mathematical basis for quantum theory and a mode of observation in the double slit experiment. This book then describes the Lorentz particle system and other mathematical structures with which fundamental quantum theory must deal, and then some unsolved problems in the quantum logic approach to the foundations of quantum mechanics are considered. Considerable chapters cover topics on manuals and logics for quantum mechanics. This book also examines the problems in quantum logic, and then presents examples of their interpretation and relevance to nonclassical logic and statistics. The accommodation of conventional Fermi-Dirac and Bose-Einstein statistics in quantum mechanics or quantum field theory is illustrated. The final chapters of the book present a system of axioms for nonrelativistic quantum mechanics, with particular emphasis on the role of density operators as states. Specific connections of this theory with other formulations of quantum theory are also considered. These chapters also deal with the determination of the state of an elementary quantum mechanical system by the associated position and momentum distribution. This book is of value to physicists, mathematicians, and researchers who are interested in quantum theory. |
Contents
| 1 | |
| 9 | |
A New Model for the 12Spin Particle and the Hydrogen Atom | 49 |
Chapter 4 Orthomodular Structures and Physical Theory | 59 |
Chapter 5 Another Nonstandard Quantum Logic and How I Found It | 71 |
Chapter 6 Some Unsolved Problems in Quantum Logics | 87 |
Chapter 7 Manuals Morphisms and Quantum Mechanics | 105 |
Chapter 8 Limits of Manuals and Logics | 127 |
Chapter 12 The Nikodym Hahn VitaleSaks Theorem for States on a Quantum Logic | 275 |
Chapter 13 On Geometric Quantization of Classical Systems | 287 |
Chapter 14 Measures with Minimum Uncertainty on NonCommutative Algebras with Application to Measurement Theory in Quantum Mechanics | 299 |
Chapter 15 Duality for CAlgebras | 329 |
Chapter 16 Geometrodynamics as Foundation of Physics | 339 |
Chapter 17 Spin and Statistics of Elementary Particles | 347 |
Chapter 18 Quantum Mechanics with Density Operators | 351 |
Chapter 19 Pure States Mixtures and Compounds | 357 |
Chapter 9 The Geometry of the State Space | 153 |
Empirical Logic Talks Quantum Mechanics | 177 |
A Nonclassical Example | 255 |
Chapter 20 Position and Momentum Distributions Do Not Determine the Quantum Mechanical State | 365 |
Other editions - View all
Common terms and phrases
1978 by Academic admits a classical amplitude axioms Banach space base-norm beam Boolean algebra Borel C*-algebra C*-bundle called classical interpretation coherent commutative conditioning strategy convex combination corresponding countably additive Dacey manual defined denoted density operator dispersion free elements Empirical Logic equation equivalent event example exists experiment finite Foulis Foundations of Quantum full set given Greechie hence Hilbert space homomorphism implies incoherent coarsenings induced isomorphic Lemma Let G linear manual G Math metric momentum morphism Neumann algebra norm observables orthogonal sets orthologic orthomodular lattice orthomodular poset outcome particle photon Phys physical polarization positive probability measure Proof proposition pure quantization quantum logic quantum mechanics quantum theory Randall representation result rotation Rüttimann satisfies self-adjoint operator sequence slit spin statistics Stern–Gerlach experiment structure subset subspace Suppose symmetry Theorem tion topology unique unitary University of Massachusetts vector weight function Weyl algebra width