Quantum Mechanics on Phase Space

Abstract

Preface. I: Basic quantum theory and the necessity for its revision. I.1. Classical mechanics of particles and fluids. I.2. Structure of a physical model: state, property (observable), measurement. I.3. Quantum mechanics of a (non-relativistic spinless) particle. I.4. On the connection between classical mechanics and quantum mechanics. I.5. Mathematical appendix. II: Basic experiments suggest generalizing quantum mechanics. II.1. Quantum mechanical descriptions of an experiment. II.2. Capture on a screen, in a bubble chamber, gel, cloud chamber. II.3. The Stern-Gerlach experiment. II.4. Crossed polarizers. II.5. Single slit experiments and inapplicability of Heisenberg uncertainty relations. II.6. Spontaneous decay, Breit-Wigner (Cauchy) distributions, and the inapplicability of Heisenberg type uncertainty relations. II.7. Interferometers. II.8. Imaging processes and signal analysis. II.9. Sensory perception and neuroscience. II.10. Five other subjects and their implications. II.11. Mathematical appendix. III: Construction of quantum mechanics on phase space. III.1. Group representation theory. III.2. The Heisenberg group (Weyl algebra) and the Affine group. III.3. Representations of the Galilei group. III.4. Representations of the Poincare group. III.5. Remarks on the de Sitter group. IV: Consequences of formulating quantum mechanics on phase space. IV.1. The quantum/classical connection. IV.2. Quantum field theory. IV.3. Spring cleaningin the house of quantum mechanics. IV.4. Reprise: Expanding the realm of application of quantum mechanics. IV.5. A discrete (lattice) quantum universe, and computability. V: Foundational aspects. V.1. Relation to generalized quantum logic. V.2. P.O.V.M.'s arising on operational manuals. V.3. Relation to quantum mechanical measurement theory. V.4. Philosophical and other foundational aspects. References. Index.