Quantum Social Science.

By: Haven, EmmanuelContributor(s): Khrennikov, AndreiPublisher: Cambridge : Cambridge University Press, 2013Copyright date: ©2013Description: 1 online resource (306 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9781139844772Subject(s): Social sciences -- Mathematical models.;Quantum theoryGenre/Form: Electronic books. Additional physical formats: Print version:: Quantum Social ScienceDDC classification: 300.153 LOC classification: H61.25 .H38 2013Online resources: Click to View
Contents:
Intro -- Contents -- Foreword -- Preface -- Acknowledgements -- List of symbols -- I Physics concepts in social science? A discussion -- 1 Classical, statistical, and quantum mechanics: all in one -- 1.1 Newtonian mechanics -- 1.2 References -- 1.3 The Hamiltonian formalism -- 1.4 Statistical mechanics and the Liouville equation -- 1.5 The classical kingdom . . . -- 1.6 References -- 1.7 Classical fields -- 1.8 Reference -- 1.9 The Born-Sommerfeld quantization -- 1.10 Reference -- 1.11 Theory of quantum waves -- 1.12 References -- 1.13 Heisenberg's symbolic calculus -- 1.14 Heisenbergian symbolism in physics: a version of symbolism in art -- 1.15 References -- 1.16 Completeness of quantum mechanics and a possibility to apply quantum mechanics outside of physics -- 1.17 References -- 1.18 Brownian motion -- 1.19 References -- 1.20 The Schr¨odinger equation -- 1.21 References -- 1.22 Do not be afraid of no-go theorems! -- 1.23 References -- 2 Econophysics: statistical physics and social science -- 2.1 Science and social science: econophysics? -- 2.2 References -- 2.3 The physics-based "Fokker-Planck" PDE in economics -- 2.4 References -- 2.5 Potential and kinetic energy in social science -- 2.6 References -- 2.7 The backward Kolmogorov PDE in finance -- 2.8 References -- 2.9 What a weird world! Martingales and fake probabilities -- 2.10 References -- 2.11 Whetting the quantum appetite -- 2.12 References -- 3 Quantum social science: a non-mathematical motivation -- 3.1 What is quantum social science? -- 3.2 Key findings from quantum social science -- 3.3 References -- II Mathematics and physics preliminaries -- 4 Vector calculus and other mathematical preliminaries -- 4.1 Linear spaces -- 4.2 References -- 4.3 State space: Hilbert space -- 4.4 References -- 4.5 Operators -- 4.6 References -- 4.7 Dirac brakets and bras and kets -- 4.8 References.
4.9 Eigenvalues/eigenfunction -- 4.10 References -- 4.11 Hermiticity -- 4.12 References -- 4.13 Projection operators -- 4.14 Probability density functions -- 4.15 References -- 4.16 ODEs and PDEs -- 4.17 References -- 4.18 Basics of stochastic mathematics, Brownian motion, non-arbitrage condition, Itˆo's Lemma -- 4.19 References -- 5 Basic elements of quantum mechanics -- 5.1 Mathematical formalism of quantum mechanics: brief introduction -- 5.2 References -- 5.3 Double slit experiment: rationale for the existence of probability waves -- 5.4 References -- 5.5 Quantum mechanical postulates -- 5.6 References -- 5.7 States and state functions -- 5.8 References -- 5.9 Wave packets - constructive and destructive interference -- 5.10 References -- 5.11 Heisenberg's uncertainty principle -- 5.12 References -- 5.13 The time-dependent and time-independent Schr¨odinger PDE -- 5.14 References -- 5.15 Classical limit ideas: Ehrenfest's approach and the correspondence principle -- 5.16 References -- 6 Basic elements of Bohmian mechanics -- 6.1 Short introduction to Bohmian mechanics -- 6.2 References -- 6.3 Mathematical formalism -- 6.4 References -- 6.5 Non-locality -- 6.6 References -- 6.7 Criticisms of Bohmian mechanics -- 6.8 References -- III Quantum probabilistic effects in psychology: basic questions and answers -- 7 A brief overview -- 7.1 Decision making in social science: general overview -- 7.2 References -- 7.3 Modeling risk: some basic approaches -- 7.4 References -- 7.5 Possible remedies to the paradox: a brief discussion -- 7.6 References -- 7.7 The role of the law of total probability (LTP): a brief overview -- 7.8 Reference -- 8 Interference effects in psychology - an introduction -- 8.1 Classical decision making and the Bayesian approach -- 8.2 References.
8.3 Non-classical decision making: violation of the LTP (law of total probability) and the quantum Bayesian approach -- 8.4 Contextual probabilistic formalization -- 8.5 Interference effects in social science: decision making based on LTP with interference terms -- 8.6 Savage sure-thing principle -- 8.7 Behavioral games: Prisoner's Dilemma -- 8.8 Violation of rationality in the experiments of Shafir and Tversky -- 8.9 Prisoner's dilemma-type experiment: Shafir and Tversky -- 8.10 Violation of double stochasticity for matrices of transition probabilities -- 8.11 Prisoner's dilemma-type experiment: Croson -- 8.12 Gambling experiment - 1: Tversky and Shafir -- 8.13 Gambling experiment - 2: Tversky and Shafir -- 8.14 The Hawaii vacation experiment -- 8.15 Non-classicality of statistical data: non-zero coefficients of interference -- 8.16 The constructive wave function approach and fit to data from the experiments of Shafir and Tversky -- 8.17 Other experiments -- 8.18 References -- 9 A quantum-like model of decision making -- 9.1 Introduction -- 9.2 Two-player game and rational behavior -- 9.3 Construction of a mental state -- 9.4 A process of decision making -- 9.5 Example: decision making in PD -- Appendix 1: Channels and liftings -- Appendix 2: Quantum Markov chain description of data from experiments in cognitive psychology -- 9.6 References -- IV Other quantum probabilistic effects in economics, finance, and brain sciences -- 10 Financial/economic theory in crisis -- 10.1 Relevance of the concepts of efficiency and non-arbitrage: a brief discussion -- 10.2 References -- 10.3 George Soros' interpretation of the crisis and the use of classical quantum physics in finance -- 10.4 References -- 10.5 The need for an information modeling device in economics and finance -- 10.6 Reference -- 11 Bohmian mechanics in finance and economics.
11.1 The pilot wave function and its uses outside of quantum mechanics -- 11.2 References -- 12 The Bohm-Vigier model and path simulation -- 12.1 The Bohm-Vigier model in finance -- 12.2 References -- 12.3 The Newton-Bohm equation: path simulation -- 12.4 Reference -- 13 Other applications to economic/financial theory -- 13.1 The (non-)Hermiticity of finance-based operators? -- 13.2 References -- 13.3 Implications of the non-Hermiticity of a Black-Scholes Hamiltonian operator on the use of the classical limit arguments -- 13.4 References -- 13.5 Implications of the non-Hermiticity of a Black-Scholes Hamiltonian operator on the stochastic equivalent of Hamilton-Jacobi equations -- 13.6 Interpretations of the wave function: a brief discussion -- 13.7 The wave function and non-observed state prices -- 13.8 Price and superposition of values -- 13.9 References -- 13.10 Arbitrage and negative probabilities -- 13.11 References -- 13.12 The Li-Zhang and WKB approach -- 13.13 References -- 13.14 The wave function as a Radon-Nikodym derivative -- 13.15 References -- 13.16 Universal Brownian motion: definition and discussion -- 13.17 References -- 13.18 Universal Brownian motion and option pricing -- 13.19 References -- 13.20 Wave functions in drift-dependent option pricing -- 13.21 References -- 13.22 Generalizations of It stochastics: path integration and other tools -- 13.23 References -- 13.24 q-calculus and finance -- 13.25 References -- 14 Neurophysiological sources of quantum-like processing in the brain -- 14.1 Introduction -- 14.2 Why could the brain use the quantum-like representation of information which is based on classical electromagnetic waves? -- 14.3 Prequantum classical statistical field theory: non-composite systems -- 14.4 Cognitive model: two regimes of brain's functioning -- 14.5 Classical regime: time representation.
14.6 Classical signal processing of mental images -- 14.7 Quantum-like processing of mental images -- 14.8 Composite systems -- 14.9 References -- 15 Conclusion -- Glossary of mathematics, physics, and economics/finance terms -- Index.
Summary: Aimed at economists and psychologists, as well as physicists, this book explores the exciting field of quantum social science.
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Intro -- Contents -- Foreword -- Preface -- Acknowledgements -- List of symbols -- I Physics concepts in social science? A discussion -- 1 Classical, statistical, and quantum mechanics: all in one -- 1.1 Newtonian mechanics -- 1.2 References -- 1.3 The Hamiltonian formalism -- 1.4 Statistical mechanics and the Liouville equation -- 1.5 The classical kingdom . . . -- 1.6 References -- 1.7 Classical fields -- 1.8 Reference -- 1.9 The Born-Sommerfeld quantization -- 1.10 Reference -- 1.11 Theory of quantum waves -- 1.12 References -- 1.13 Heisenberg's symbolic calculus -- 1.14 Heisenbergian symbolism in physics: a version of symbolism in art -- 1.15 References -- 1.16 Completeness of quantum mechanics and a possibility to apply quantum mechanics outside of physics -- 1.17 References -- 1.18 Brownian motion -- 1.19 References -- 1.20 The Schr¨odinger equation -- 1.21 References -- 1.22 Do not be afraid of no-go theorems! -- 1.23 References -- 2 Econophysics: statistical physics and social science -- 2.1 Science and social science: econophysics? -- 2.2 References -- 2.3 The physics-based "Fokker-Planck" PDE in economics -- 2.4 References -- 2.5 Potential and kinetic energy in social science -- 2.6 References -- 2.7 The backward Kolmogorov PDE in finance -- 2.8 References -- 2.9 What a weird world! Martingales and fake probabilities -- 2.10 References -- 2.11 Whetting the quantum appetite -- 2.12 References -- 3 Quantum social science: a non-mathematical motivation -- 3.1 What is quantum social science? -- 3.2 Key findings from quantum social science -- 3.3 References -- II Mathematics and physics preliminaries -- 4 Vector calculus and other mathematical preliminaries -- 4.1 Linear spaces -- 4.2 References -- 4.3 State space: Hilbert space -- 4.4 References -- 4.5 Operators -- 4.6 References -- 4.7 Dirac brakets and bras and kets -- 4.8 References.

4.9 Eigenvalues/eigenfunction -- 4.10 References -- 4.11 Hermiticity -- 4.12 References -- 4.13 Projection operators -- 4.14 Probability density functions -- 4.15 References -- 4.16 ODEs and PDEs -- 4.17 References -- 4.18 Basics of stochastic mathematics, Brownian motion, non-arbitrage condition, Itˆo's Lemma -- 4.19 References -- 5 Basic elements of quantum mechanics -- 5.1 Mathematical formalism of quantum mechanics: brief introduction -- 5.2 References -- 5.3 Double slit experiment: rationale for the existence of probability waves -- 5.4 References -- 5.5 Quantum mechanical postulates -- 5.6 References -- 5.7 States and state functions -- 5.8 References -- 5.9 Wave packets - constructive and destructive interference -- 5.10 References -- 5.11 Heisenberg's uncertainty principle -- 5.12 References -- 5.13 The time-dependent and time-independent Schr¨odinger PDE -- 5.14 References -- 5.15 Classical limit ideas: Ehrenfest's approach and the correspondence principle -- 5.16 References -- 6 Basic elements of Bohmian mechanics -- 6.1 Short introduction to Bohmian mechanics -- 6.2 References -- 6.3 Mathematical formalism -- 6.4 References -- 6.5 Non-locality -- 6.6 References -- 6.7 Criticisms of Bohmian mechanics -- 6.8 References -- III Quantum probabilistic effects in psychology: basic questions and answers -- 7 A brief overview -- 7.1 Decision making in social science: general overview -- 7.2 References -- 7.3 Modeling risk: some basic approaches -- 7.4 References -- 7.5 Possible remedies to the paradox: a brief discussion -- 7.6 References -- 7.7 The role of the law of total probability (LTP): a brief overview -- 7.8 Reference -- 8 Interference effects in psychology - an introduction -- 8.1 Classical decision making and the Bayesian approach -- 8.2 References.

8.3 Non-classical decision making: violation of the LTP (law of total probability) and the quantum Bayesian approach -- 8.4 Contextual probabilistic formalization -- 8.5 Interference effects in social science: decision making based on LTP with interference terms -- 8.6 Savage sure-thing principle -- 8.7 Behavioral games: Prisoner's Dilemma -- 8.8 Violation of rationality in the experiments of Shafir and Tversky -- 8.9 Prisoner's dilemma-type experiment: Shafir and Tversky -- 8.10 Violation of double stochasticity for matrices of transition probabilities -- 8.11 Prisoner's dilemma-type experiment: Croson -- 8.12 Gambling experiment - 1: Tversky and Shafir -- 8.13 Gambling experiment - 2: Tversky and Shafir -- 8.14 The Hawaii vacation experiment -- 8.15 Non-classicality of statistical data: non-zero coefficients of interference -- 8.16 The constructive wave function approach and fit to data from the experiments of Shafir and Tversky -- 8.17 Other experiments -- 8.18 References -- 9 A quantum-like model of decision making -- 9.1 Introduction -- 9.2 Two-player game and rational behavior -- 9.3 Construction of a mental state -- 9.4 A process of decision making -- 9.5 Example: decision making in PD -- Appendix 1: Channels and liftings -- Appendix 2: Quantum Markov chain description of data from experiments in cognitive psychology -- 9.6 References -- IV Other quantum probabilistic effects in economics, finance, and brain sciences -- 10 Financial/economic theory in crisis -- 10.1 Relevance of the concepts of efficiency and non-arbitrage: a brief discussion -- 10.2 References -- 10.3 George Soros' interpretation of the crisis and the use of classical quantum physics in finance -- 10.4 References -- 10.5 The need for an information modeling device in economics and finance -- 10.6 Reference -- 11 Bohmian mechanics in finance and economics.

11.1 The pilot wave function and its uses outside of quantum mechanics -- 11.2 References -- 12 The Bohm-Vigier model and path simulation -- 12.1 The Bohm-Vigier model in finance -- 12.2 References -- 12.3 The Newton-Bohm equation: path simulation -- 12.4 Reference -- 13 Other applications to economic/financial theory -- 13.1 The (non-)Hermiticity of finance-based operators? -- 13.2 References -- 13.3 Implications of the non-Hermiticity of a Black-Scholes Hamiltonian operator on the use of the classical limit arguments -- 13.4 References -- 13.5 Implications of the non-Hermiticity of a Black-Scholes Hamiltonian operator on the stochastic equivalent of Hamilton-Jacobi equations -- 13.6 Interpretations of the wave function: a brief discussion -- 13.7 The wave function and non-observed state prices -- 13.8 Price and superposition of values -- 13.9 References -- 13.10 Arbitrage and negative probabilities -- 13.11 References -- 13.12 The Li-Zhang and WKB approach -- 13.13 References -- 13.14 The wave function as a Radon-Nikodym derivative -- 13.15 References -- 13.16 Universal Brownian motion: definition and discussion -- 13.17 References -- 13.18 Universal Brownian motion and option pricing -- 13.19 References -- 13.20 Wave functions in drift-dependent option pricing -- 13.21 References -- 13.22 Generalizations of It stochastics: path integration and other tools -- 13.23 References -- 13.24 q-calculus and finance -- 13.25 References -- 14 Neurophysiological sources of quantum-like processing in the brain -- 14.1 Introduction -- 14.2 Why could the brain use the quantum-like representation of information which is based on classical electromagnetic waves? -- 14.3 Prequantum classical statistical field theory: non-composite systems -- 14.4 Cognitive model: two regimes of brain's functioning -- 14.5 Classical regime: time representation.

14.6 Classical signal processing of mental images -- 14.7 Quantum-like processing of mental images -- 14.8 Composite systems -- 14.9 References -- 15 Conclusion -- Glossary of mathematics, physics, and economics/finance terms -- Index.

Aimed at economists and psychologists, as well as physicists, this book explores the exciting field of quantum social science.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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