Contextual Approach to Quantum Formalism

Part I: Quantum and Classical ProbabilityChapter 1: Quantum Mechanics: Postulates and Interpretations1.1 Quantum Mechanics 1.1.1 Mathematical Basis 1.1.2 Postulates 1.2 Projection Postulate, Collapse of Wave Function, Schr\'odinger's Cat 1.2.1 Von Neumann's Projection Postulate 1.2.2 Collapse of Wave Function 1.2.3 Schr\'odinger's Cat 1.2.4 L\'uders Projection Postulate 1.3 Statistical Mixtures 1.4 Von Neumann's and L\'uders' Postulates for Mixed States1.5 Conditional Probability1.6 Derivation of Interference of Probabilities Chapter 2: Classical Probability Theories2.1 Kolmogorov Measure-Theoretic Model 2.1.1 Formalism 2.1.2 Discussion 2.2 Von Mises Frequency Model 2.2.1 Collective (Random Sequence) 2.2.2 Difficulties with Definition of Randomness 2.2.3 $S$-sequences 2.2.4 Operations for Collectives 2.3 Combining and Independence of Collectives Part I I: Contextual Probability and\\ Quantum-Like Models Chapter 1: Contextual Probability and Interference1.1 V\'axj\'o model: Contextual Probability 1.1.1 Contexts 1.1.2 Observables 1.1.3 Contextual Probability Space and Model 1.1.4 V\'axj\'o Models Induced by the Kolmogorov Model 1.1.5 V\'axj\'o Models Induced by QM 1.1.6 V\'axj\'o Models Induced by the von Mises Model 1.2 Contextual Probabilistic Description of Double Slit Experiment 1.3 Formula of Total Probability and Measures of Supplementarity 1.4 Supplementary Observables 1.5 Principle of Supplementarity 1.6 Supplementarity and Kolmogorovness 1.6.1 Double Stochasticity as the Law of Probabilistic Balance 1.6.2 Probabilistically Balanced Observables 1.6.3 Symmetrically Conditioned Observables 1.7 Incompatibility, Supplementarity and Existence of Joint Probability Distribution 1.7.1 Joint Probability Distribution 1.7.2 Incompatible and Supplementary Observables 1.7.3 Compatibility and Probabilistic Compatibility 1.8 Interpretational Questions 1.8.1 Contextuality 1.8.2 Realism 1.9 Historical Remark: Comparing with Mackey's Model1.10 Subjective and Contextual

Prof. Andrei Khrennikov is the director of International center for mathematical modeling in physics, engineering and cognitive science, University of Växjö, Sweden, which was created 8 years ago to perform interdisciplinary research.

Two series of conferences on quantum foundations (especially probabilistic aspects) were established on the basis of this center: "Foundations of Probability and Physics" and "Quantum Theory: Reconsideration of Foundations". These series became well known in the quantum community (including quantum information groups). Hundreds of theoreticians (physicists and mathematicians), experimenters and even philosophers participated in these conferences presenting a huge diversity of views to quantum foundations. Contacts with these people played the crucial role in creation of the present book.Prof. Andrei Khrennikov published about 300 papers in internationally recognized journals in mathematics, physics and biology and 9 monographs - in p-adic and non-Archimedean analysis with applications to mathematical physics and cognitive sciences as well as foundations of probabilityu theory.

From the reviews:"In this book the author presents an unorthodox account of quantum probability theory according to which all the latter's key features can be reproduced and brought under a common formalism (known as the 'Växjö model') with classical statistical mechanics by using a formalism based on contextual probability ... . the ideas contained in this book are of potentially very high importance." (Dean Rickles, Mathematical Reviews, Issue 2011 i)