Preface	6
	Acknowledgements	8
	Contents	10
	1 Quantum-like Paradigm	16
	1.1 Applications of Mathematical Apparatus of QM Outsideof Physics	16
	1.2 Irreducible Quantum Randomness, Copenhagen Interpretation	17
	1.3 Quantum Reductionism in Biology and Cognitive Science	18
	1.4 Statistical (or Ensemble) Interpretation of QM	19
	1.5 No-Go Theorems	20
	1.6 Einstein's and Bohr's Views on Realism	21
	1.7 Quantum and Quantum-like Models	22
	1.8 Quantum-like Representation Algorithm -- QLRA	22
	1.9 Non-Kolmogorov Probability	23
	1.10 Contextual Probabilistic Model -- Växjö Model	24
	1.11 Experimental Verification	25
	1.12 Violation of Savage's Sure Thing Principle	26
	1.13 Quantum-like Description of the Financial Market	26
	1.14 Quantum and Quantum-like Games	28
	1.15 Terminology: Context, Contextual Probability, Contextuality	29
	1.16 Formula of Total Probability	30
	1.17 Formula of Total Probability with Interference Term	30
	1.18 Quantum-like Representation of Contexts	31
	2 Classical (Kolmogorovian) and Quantum (Born) Probability	33
	2.1 Kolmogorovian Probabilistic Model	33
	2.1.1 Probability Space	33
	2.1.2 Conditional Probability	36
	2.1.3 Formula of Total Probability	38
	2.2 Probabilistic Incompatibility: Bell--Boole Inequalities	39
	2.2.1 Views of Boole, Kolmogorov, and Vorob'ev	40
	2.2.2 Bell's and Wigner's Inequalities	42
	2.2.3 Bell-type Inequalities for Conditional Probabilities	42
	2.3 Quantum Probabilistic Model	43
	2.3.1 Postulates	44
	2.3.2 Quantization	47
	2.3.3 Interpretations of Wave Function	48
	2.4 Quantum Conditional Probability	49
	2.5 Interference of Probabilities in Quantum Mechanics	50
	2.6 Contextual Point of View of Interference	52
	2.7 Bell's Inequality in Quantum Physics	52
	2.8 Växjö Interpretation of Quantum Mechanics	54
	3 Contextual Probabilistic Model -- Växjö Model	55
	3.1 Contextual Description of Observations	55
	3.1.1 Contextual Probability Space and Model	55
	3.1.2 Selection Contexts	57
	3.1.3 Transition Probabilities, Reference Observables	57
	3.1.4 Covariance	58
	3.1.5 Interpretations of Contextual Probabilities	59
	3.2 Formula of Total Probability with Interference Term	60
	4 Quantum-like Representation Algorithm -- QLRA	63
	4.1 Inversion of Born's Rule	64
	4.2 QLRA: Complex Representation	65
	4.3 Visualization on Bloch's Sphere	69
	4.4 The Case of Non-Doubly Stochastic Matrices	71
	4.5 QLRA: Hyperbolic Representation	72
	4.5.1 Hyperbolic Born's Rule	72
	4.5.2 Hyperbolic Hilbert Space Representation	74
	4.6 Bloch's Hyperboloid	75
	5 The Quantum-like Brain	79
	5.1 Quantum and Quantum-like Cognitive Models	79
	5.2 Interference of Minds	82
	5.2.1 Cognitive and Social Contexts	82
	5.2.2 Quantum-like Structure of Experimental Mental Data	83
	5.2.3 Contextual Redundancy	84
	5.2.4 Mental Wave Function	86
	5.3 Quantum-like Projection of Mental Reality	86
	5.3.1 Social Opinion Poll	86
	5.3.2 Quantum-like Functioning of Neuronal Structures	87
	5.4 Quantum-like Consciousness	89
	5.5 The Brain as a Quantum-like Computer	90
	5.6 Evolution of Mental Wave Function	90
	5.6.1 Structure of a Set of Mental States	91
	5.6.2 Combining Neuronal Realism with Quantum-like Formalism	92
	6 Experimental Tests of Quantum-like Behavior of the Mind	93
	6.1 Theoretical Foundations of Experiment	93
	6.2 Gestalt Perception Theory	94
	6.3 Gestalt-like Experiment for Quantum-like Behavior of the Mind	95
	6.4 Analysis of Cognitive Entities	98
	6.5 Description of Experiment on Image Recognition	100
	6.5.1 Preparation	101
	6.5.2 First Experiment: Slight Deformations Versus ShortExposure Time	101
	6.5.3 Second Experiment: Essential Deformations VersusLong Exposure Time	102
	6.6 Interference Effect at the Financial Market?	104
	6.6.1 Supplementary (``complementary'') Stocks	104
	6.6.2 Experiment Design	105
	7 Quantum-like Decision Making and Disjunction Effect	107
	7.1 Sure Thing Principle, Disjunction Effect	107
	7.2 Quantum-like Decision Making: General Discussion and Postulates	110
	7.2.1 Superposition of Choices	112
	7.2.2 Parallelism of Creation and Processing of Mental Wave function	113
	7.2.3 Quantum-like Rationality	113
	7.2.4 Quantum-like Ethics	114
	7.3 Rational Behavior, Prisoner's Dilemma	114
	7.4 Contextual Analysis of Experiments with Disjunction Effect	115
	7.4.1 Prisoner's Dilemma	115
	7.4.2 Gambling Experiment	118
	7.4.3 Exam's Result and Hawaii Experiment	119
	7.5 Reason-Based Choice and Its Quantum-like Interpretation	119
	7.6 Coefficients of Interference and Quantum-like Representation	120
	7.7 Non-double Stochasticity of Matrices of Transition Probabilities in Cognitive Psychology	121
	7.8 Decision Making	122
	7.9 Bayesian Updating of Mental State Distribution	124
	7.10 Mixed State Representation	126
	7.11 Comparison with Standard Quantum Decision-Making Theory	126
	7.12 Bayes Risk	127
	7.13 Conclusion	128
	8 Macroscopic Games and Quantum Logic	129
	8.1 Spin-One-Half Example of a Quantum-like Game	131
	8.2 Spin-One Quantum-like Game	136
	8.3 Interference of Probability in Quantum-like Games	141
	8.4 Wave Functions in Macroscopic Quantum-like Games	143
	8.5 Spin-One-Half Game with Three Observables	146
	8.6 Heisenberg's Uncertainty Relations	148
	8.7 Cooperative Quantum-like Games, Entanglement	149
	9 Contextual Approach to Quantum-like Macroscopic Games	150
	9.1 Quantum Probability and Game Theory	150
	9.2 Wine Testing Game	151
	9.3 Extensive Form Game with Imperfect Information	154
	9.3.1 Quantum-like Representation of the Wine Testing Game	155
	9.3.2 Superposition of Preferences	156
	9.3.3 Interpretation of Gambling Wave Function	156
	9.3.4 The Role of Bayes Formula	157
	9.3.5 Action at a Distance?	158
	9.4 Wine Game with Three Players	158
	9.5 Simulation of the Wine Game	159
	9.6 Bell's Inequality for Averages of Payoffs	160
	10 Psycho-financial Model	163
	10.1 Deterministic and Stochastic Models of Financial Markets	163
	10.1.1 Efficient Market Hypothesis	163
	10.1.2 Deterministic Models for Dynamics of Prices	164
	10.1.3 Behavioral Finance and Economics	165
	10.1.4 Quantum-like Model for Behavioral Finance	166
	10.2 Classical Econophysical Model of the Financial Market	167
	10.2.1 Financial Phase Space	167
	10.2.2 Classical Dynamics	169
	10.2.3 Critique of Classical Econophysics	171
	10.3 Quantum-like Econophysical Model of the Financial Market	172
	10.3.1 Financial Pilot Waves	172
	10.3.2 Dynamics of Prices Guided by Financial Pilot Wave	173
	10.4 Application of Quantum Formalism to the Financial Market	177
	10.5 Standard Deviation of Price	178
	10.6 Comparison with Conventional Models of the Financial Market	179
	10.6.1 Stochastic Model	179
	10.6.2 Deterministic Dynamical Model	181
	10.6.3 Stochastic Model and Expectations of Agents of the Financial Market	182
	11 The Problem of Smoothness of Bohmian Trajectories	183
	11.1 Existence Theorems for Nonsmooth Financial Forces	183
	11.1.1 The Problem of Smoothness of Price Trajectories	183
	11.1.2 Picard's Theorem and its Generalization	185
	11.2 The Problem of Quadratic Variation	188
	11.3 Singular Potentials and Forces	189
	11.3.1 Example	189
	11.3.2 Singular Quantum Potentials	189
	11.4 Classical and Quantum Financial Randomness	190
	11.4.1 Randomness of Initial Conditions	191
	11.4.2 Random Financial Mass	191
	11.5 Bohm--Vigier Stochastic Mechanics	192
	11.6 Bohmian Model and Models with Stochastic Volatility	194
	11.7 Classical and Quantum Contributions to Financial Randomness	195
	12 Appendix	196
	12.1 Independence	196
	12.1.1 Kolmogorovian Model	196
	12.1.2 Quantum Model	197
	12.1.3 Växjö Model	198
	12.2 Proof of Wigner's Inequality	199
	12.3 Projection Postulate	201
	12.4 Contextual View of Kolmogorov and Quantum Models	201
	12.4.1 Contextual Models Induced by the Classical (Kolmogorov) Model	201
	12.4.2 Contextual Models Induced by the Quantum (Dirac--von neumann) Model	202
	12.5 Generalization of Quantum Formalism	202
	12.6 Bohmian Mechanics	205
	References	209
	Index	223