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E-raamat: Quantum Methods In Social Science: A First Course

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(Linnaeus Univ, Sweden), (Univ Of Leicester, Uk), (Univ Of Leicester, Uk)
  • Formaat: 276 pages
  • Ilmumisaeg: 22-Jun-2017
  • Kirjastus: World Scientific Europe Ltd
  • Keel: eng
  • ISBN-13: 9781786342799
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Quantum Methods In Social Science: A First CourseSuurem pilt
  • Formaat: 276 pages
  • Ilmumisaeg: 22-Jun-2017
  • Kirjastus: World Scientific Europe Ltd
  • Keel: eng
  • ISBN-13: 9781786342799
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Shown here is how basic concepts of physics can be used to improve models in finance, economics, psychology and biology. Readers are introduced to how physical theory can inform non-physical phenomena in the social sciences, thereby improving decision making and modelling capabilities in research-based and professional settings.Consisting of three parts, the first part deals with the application of quantum operator methods to financial transactions and population dynamics. Part two develops physical concepts, working from classical Lagrangian and Hamiltonian mechanics and leading to an introduction of quantum information and its application to decision making. The final part treats classical and quantum probability theory in some detail and deals, at a more advanced level, with the impact of quantum probabilities on common knowledge and common beliefs between agents in systems.Quantum Methods in Social Science is a high level textbook for advanced undergraduate or graduate students of economics, finance and business, while also being of interest to those with a background in physics.
Preface xv
About the Authors xix
Part I: Quantum Counting: The Number Operator in a Social Science Context 1(96)
1 Introduction
3(16)
1.1 What's it all about?
3(8)
1.1.1 Three versions of physics
5(2)
1.1.2 Quantizing classical physics
7(1)
1.1.3 Quantum numbers
8(1)
1.1.4 Quantum field theory
9(2)
1.2 Counting in culture, society, and science
11(3)
1.2.1 As simple as 1, 2, 3
11(2)
1.2.2 And then there were none
13(1)
1.3 Classical or quantum representation?
14(5)
1.3.1 Data and information
14(1)
1.3.2 Representation I: The classical way
14(1)
1.3.3 Representation II: The quantum way
15(1)
1.3.4 Second quantization and how to count things
16(3)
2 Classical Interlude: Modeling Population Dynamics
19(10)
2.1 Population growth and decay: Just rabbits
20(1)
2.2 Introducing a second species: Enter the foxes
21(2)
2.3 Some observations on the Lotka-Volterra model
23(6)
2.3.1 Fluctuating population numbers
23(2)
2.3.2 Eliminating one of the variables
25(1)
2.3.3 Integral of the motion and conserved quantities
26(1)
2.3.4 Range of applications
27(2)
3 A Quantum Description of Systems
29(16)
3.1 Operators, states, and eigenvalues
29(3)
3.1.1 The Schrodinger equation
29(1)
3.1.2 Linear operators
30(1)
3.1.3 Eigenvalue equations
31(1)
3.1.4 Expectation values, normalization, and orthogonality
32(1)
3.2 Dirac notation
32(1)
3.3 Some special operator properties
33(7)
3.3.1 Adjoint operators
33(2)
3.3.2 Hermitian operators
35(1)
3.3.3 Operator functions
36(2)
3.3.4 When do operators commute?
38(1)
3.3.5 Expansion of commutation brackets
39(1)
3.3.6 Positive operators
39(1)
3.4 Heisenberg operators
40(2)
3.5 Exercises
42(3)
4 Quantum Counting
45(12)
4.1 The mechanics of counting
45(4)
4.1.1 Repetition, cyclic processes, and clocks
46(2)
4.1.2 Phasors: The complex plane as a clock counter
48(1)
4.2 Generating a spectrum of integers with the integer operator
49(1)
4.3 Generating a spectrum of natural numbers with the number operator
50(3)
4.4 Occupation number notation and properties of a and a+
53(4)
4.4.1 Occupation number notation
53(1)
4.4.2 Everything stops at zero
54(1)
4.4.3 Building the state |n) from scratch
55(1)
4.4.4 Commutation brackets with functions of a and a+
55(2)
5 Quantum Transactions
57(26)
5.1 The quantum trader
57(1)
5.2 Several non-trading traders
58(2)
5.3 Allowing the traders to trade
60(1)
5.4 A simple transaction model: Two traders
61(4)
5.4.1 Setting up the Hamiltonian
61(1)
5.4.2 Applying the HEM to the population numbers
61(1)
5.4.3 A direct method of solution
62(3)
5.5 Key characteristics of the simple quantum two-trader model
65(2)
5.6 Eigenfrequency approach
67(4)
5.7 Stable trading partnerships
71(1)
5.8 Several trading traders
72(3)
5.8.1 A three-trader example
72(3)
5.9 Independent subsystems: Worlds within worlds
75(1)
5.10 Asymmetrical trading
76(4)
5.10.1 Different exchange rates
76(1)
5.10.2 A new integrals of the motion
77(1)
5.10.3 A worked example, P = 1, Q = 2
78(1)
5.10.4 An approximate solution
79(1)
5.11 Exercises
80(3)
6 Quantum Migration
83(4)
6.1 Nearest neighbor hopping in one dimension
83(3)
6.2 Exercises
86(1)
7 More Elaborate Systems
87(6)
7.1 Buying and selling models
87(1)
7.2 Integrals of the motion
88(1)
7.3 Solving the equations of motion
89(1)
7.4 Further refinements: Supply and price
90(3)
8 Conclusions
93(2)
References-Part I
95(2)
Part II: The Quantum-Like Paradigm with Simple Applications 97(66)
9 Taking a Step Back
99(32)
9.1 Introduction
99(4)
9.2 Some basic ideas from classical mechanics
103(6)
9.2.1 Energy conservation
103(1)
9.2.2 First analogs with social science
104(1)
9.2.3 The Lagrangian and the action functional
105(1)
9.2.4 The birth of the Hamiltonian
106(1)
9.2.5 Momentum conservation in finance?
107(2)
9.2.6 Conservation: How important is it?
109(1)
9.3 Applying basic classical mechanics to finance and economics: Some examples
109(8)
9.3.1 Example 1: A synergetics approach in behavioral economics
109(2)
9.3.2 Example 2: An action functional and arbitrage
111(2)
9.3.3 Example 3: Re-modeling equilibrium pricing with a Lagrangian framework
113(4)
9.4 Option pricing and physics based partial differential equations
117(14)
9.4.1 What are options?
117(1)
9.4.2 Brownian motion and Einstein
118(4)
9.4.3 Exercises
122(1)
9.4.4 Some toolkit concepts, which relate to stochastics
123(1)
9.4.5 Taylor series adapted for stochastic processes
124(2)
9.4.6 Exercises
126(1)
9.4.7 'Option pricing: The stochastic approach
126(2)
9.4.8 Exercises
128(3)
10 Modeling Information with an Operational Formalism
131(22)
10.1 Elementary quantum mechanics
131(2)
10.2 Elementary quantum mechanics in social science
133(7)
10.2.1 An example from finance: State prices
136(3)
10.2.2 Quantum mathematics and finance
139(1)
10.3 Non-Hermitian Hamiltonians in modern quantum physics
140(2)
10.4 Bohmian mechanics and social science?
142(11)
10.4.1 Smooth trajectories?
145(1)
10.4.2 Fisher information?
146(3)
10.4.3 Beyond analogies
149(1)
10.4.4 Exercises
150(3)
11 Decision Making and Quantum Probability
153(4)
11.1 Ellsberg paradox and elementary quantum mechanics
153(12)
11.1.1 Exercises
156(1)
References-Part II
157(6)
Part III: The Quantum-Like Paradigm with Advanced Applications 163(88)
12 Basics of Classical Probability
165(14)
12.1 Introduction
165(1)
12.2 Classical probability
166(8)
12.2.1 Bayes formula, conditional probability, and formula of total probability
170(1)
12.2.2 Interpretation of probability: Statistical, subjective and their mixing
171(1)
12.2.3 Contextuality of Kolmogorov theory
172(1)
12.2.4 Exercises
173(1)
12.3 Classical decision making through the Bayesian probability update
174(5)
12.3.1 Subjective and frequentist interpretations of classical Bayesian inference
175(2)
12.3.2 Cromwell rule
177(2)
13 Quantum Probability
179(16)
13.1 Quantum probability: Pure states
179(5)
13.1.1 Exercises
182(2)
13.2 Quantum decision making through update of the belief state
184(5)
13.2.1 Exercises
188(1)
13.3 Quantum probability: Mixed states
189(2)
13.3.1 Exercises
191(1)
13.4 Events in quantum logic
191(4)
14 Common Knowledge
195(12)
14.1 General discussion on Aumann's theorem for classical and quantum agents
198(4)
14.2 Classical probabilistic approach to common knowledge
202(5)
15 Quantum(-like) Formalization of Common Knowledge
207(16)
15.1 Quantum representation of the states of the world
207(2)
15.2 Knowing events, quantum representation
209(3)
15.2.1 Exercises
211(1)
15.3 Common knowledge, quantum representation
212(1)
15.4 Quantum state update, projection postulate
213(1)
15.5 Quantum(-like) viewpoint on the Aumann's theorem
213(8)
15.5.1 Common prior assumption
213(2)
15.5.2 Disagree from quantum(-like) interference
215(6)
15.6 Agent with information representation based on incompatible question-observables
221(2)
16 Examples
223(12)
16.1 Examples illustrating agreement on disagree
223(2)
16.1.1 Exercises
224(1)
16.2 Example: Agreement on disagree from two opinion polls
225(8)
16.2.1 Still possible to agree on the posterior probabilities
231(1)
16.2.2 Is entanglement important?
232(1)
16.2.3 Classical model
233(1)
16.3 A concluding discussion on approaching agreement between quantum agents
233(2)
17 Appendix
235(8)
17.1 Operator approach to common knowledge formalization
235(8)
17.1.1 What does it mean to know? Quantum probabilistic formulation
239(4)
References-Part III
243(8)
Index 251
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