An Axiomatic Basis for Quantum Mechanics

I The Problem of Formulating an Axiomatics for Quantum Mechanics.- § 1 Is There an Axiomatic Basis for Quantum Mechanics?.- § 2 Concepts Unsuitable in a Basis for Quantum Mechanics.- § 3 Experimental Situations Describable Solely by Pretheories.- § 4 Mathematical Problems.- § 5 Progress to More Comprehensive Theories.- II Pretheories for Quantum Mechanics.- § 1 State Space and Trajectory Space.- § 2 Preparation and Registration Procedures.- § 2.1 Statistical Selection Procedures.- § 2.2 Preparation Procedures.- § 2.3 Registration Procedures.- § 2.4 Dependence of Registration on Preparation.- § 3 Trajectory Preparation and Registration Procedures.- § 3.1 Trajectory Effects.- § 3.2 Trajectory Ensembles.- § 3.3 The Dynamic Laws and the Objectivating Manner of Description.- § 3.4 Dynamically Continuous Systems.- § 4 Transformations of Preparation and Registration Procedures.- § 4.1 Time Translations of the Trajectory Registration Procedures.- § 4.2 Time Translations of the Preparation Procedures.- § 4.3 Further Transformations of Preparation and Registration Procedures.- § 5 The Macrosystems as Physical Objects.- III Base Sets and Fundamental Structure Terms for a Theory of Microsystems.- § 1 Composite Macrosystems.- § 2 Preparation and Registration Procedures for Composite Macrosystems.- § 3 Directed Interactions.- § 4 Action Carriers.- § 5 Ensembles and Effects.- § 5.1 The Problem of Combining Preparation and Registration Procedures.- § 5.2 Physical Systems.- § 5.3 Mixing and De-mixing of Ensembles and Effects.- § 5.4 Re-elimination of the Action Carrier.- § 6 Objectivating Method of Describing Experiments.- § 6.1 The Method of Describing Composite Macrosystems in the Trajectory Space.- § 6.2 Trajectory Effects of the Composite Systems.- § 6.3 Trajectory Ensembles of the Composite Systems.- § 6.4 The Structure of the Trajectory Measures for Directed Action.- § 6.5 Complete Description by Trajectories.- § 6.6 Use of the Interaction for the Registration of Macrosystems.- § 6.7 The Relation Between the Two Forms of an Axiomatic Basis.- § 7 Transport of Systems Relative to Each Other.- IV Embedding of Ensembles and Effect Sets in Topological Vector Spaces.- § 1 Embedding of K, L in a Dual Pair of Vector Spaces.- § 2 Uniform Structures of the Physical Imprecision on K and L.- § 3 Embedding of K and L in Topologically Complete Vector Spaces.- § 4 ?, ?’, D, D’ Considered as Ordered Vector Spaces.- § 5 The Faces of K and L.- § 6 Some Convergence Theorems.- V Observables and Preparators.- § 1 Coexistent Effects and Observables.- § 1.1 Coexistent Registrations.- § 1.2 Coexistent Effects.- § 1.3 Observables.- § 2 Mixture Morphisms.- § 3 Structures in the Class of Observables.- § 3.1 The Spaces ? (?) and ?’ (?) Assigned to a Boolean Ring ?.- § 3.2 Mixture Morphism Corresponding to an Observable.- § 3.3 The Kernel of an Observable.- § 3.4 De-mixing of Observables.- § 3.5 Measurement Scales of Observables and Totally Ordered Subsets of L.- § 4 Coexistent and Complementary Observables.- § 5 Realization of Observables.- § 6 Coexistent De-mixing of Ensembles.- § 7 Complementary De-mixings of Ensembles.- § 8 Realizations of De-mixings.- § 9 Preparators and Faces of K.- § 10 Physical Objects as Action Carriers.- § 11 Operations and Transpreparators.- VI Main Laws of Preparation and Registration.- § 1 Main Laws for the Increase in Sensitivity of Registrations.- § 1.1 Increase in Sensitivity Relative to Two Effect Procedures.- § 1.2 Some Experimental and Intuitive Indications for the Law of Increase in Sensitivity.- § 1.3 Decision Effects.- § 1.4 The Increase in Sensitivity of an Effect.- § 2 Relations Between Preparation and Registration Procedures.- § 2.1 Main Law for the De-mixing of Ensembles and Related Possibilities of Registering.- § 2.2 Some Consequences of Axiom AV2.- § 3 The Lattice G.- § 4 Commensurable Decision Effects.- § 5 The Orthomodularity of G.- § 6 The Main Law for Not Coexistent Registrations.- § 6.1 Experimental Hints for Formulating the Main Law for Not Coexistent Registrations.- § 6.2 Some Important Equiválenees.- § 6.3 Formulation of the Main Law and Some Consequences.- § 7 The Main Law of Quantization.- § 7.1 Intuitive Indications for Formulating the Main Law of Quantization.- § 7.2 Simple Consequences of the Main Law of Quantization.- VII Decision Observables and the Center.- § 1 The Commutator of a Set of Decision Effects.- § 2 Decision Observables.- § 3 Structures in That Class of Observables Whose Range also Contains Elements of G.- § 4 Commensurable Decision Observables.- § 5 Decomposition of ? and ?’ Relative to the Center Z.- § 5.1 Reduction of the Elements of ?’ by the Elements of G.- § 5.2 Reduction by Center Elements.- § 5.3 Classical Systems.- § 5.4 Decomposition into Irreducible Parts.- § 6 System Types and Super Selection Rules.- VIII Representation of ?, ?’ by Banach Spaces of Operators in a Hilbert Space.- § 1 The Finite Elements of G.- § 2 The General Representation Theorem for Irreducible G.- § 3 Some Topological Properties of G.- § 4 The Representation Theorem for K, L.- § 4.1 The Representation Theorem for G.- § 4.2 The Ensembles and Effects.- § 4.3 Coexistence, Commensurability, Uncertainty Relations, and Commutability of Operators.- § 5 Some Theorems for Finite-dimensional and Irreducible ?.- A II Banach Lattices.- A III The Axiom AVid and the Minimal Decomposition Property.- A IV The Bishop-Phelps Theorem and the Ellis Theorem.- List of Frequently Used Symbols.- List of Axioms.