Quantum Methods in Social Science

A First Course

Emmanuel Haven, Andrei Khrennikov;Terry Robinson

• Publisher: WSPC (EUROPE)
• Year: 2017
• eBook ISBN: 9781786342799
• Topic: Economics
• Subtopic: Finance
• Index: Economics

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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 modeling 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.

--> Contents:

• Quantum Counting: The Number Operator in a Social Science Context:
  • Introduction
  • Classical Interlude: Modelling Population Dynamics
  • A Quantum Description of Systems
  • Quantum Counting
  • Quantum Transactions
  • Quantum Migration
  • More Elaborate Systems
  • Conclusions
  • References — Part I
• The Quantum-Like Paradigm with Simple Applications:
  • Taking a Step Back
  • Modeling Information with an Operational Formalism
  • Decision Making and Quantum Probability
  • References — Part II
• The Quantum-Like Paradigm with Advanced Applications:
  • Basics of Classical Probability
  • Quantum Probability
  • Common Knowledge
  • Quantum(-Like) Formalization of Common Knowledge
  • Examples
  • Appendix
  • References — Part III

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--> Readership: Advanced undergraduate or graduate students of economics, finance and business, while also being of interest to those with a background in physics. -->
Keywords:Quantum Formalism;Physical Theory;Hamiltonian Mechanics;Probaility Theory;Financial Modeling;Langrarian Mechanics;Quantum Operator Methods;Population DynamicsReview:0

Part I

Quantum Counting: The Number
Operator in a Social Science Context

Chapter 1

Introduction

1.1.What’s it all about?

In this part of the book, we want to introduce some quantum tools for modeling interacting systems, which can be applied to situations in social science (see [5, 7, 11, 13, 20]). We are going to borrow these tools from what is often considered to be the most fundamental physical theory, namely, quantum field theory (QFT). That QFT is seen by many people, including, it must be said, by a lot of physicists themselves, as a mind-boggling theory, far from everyday reality, understood only by a tiny handful of brilliant minds, should not daunt the reader. We do not need to know anything about the quantum theory of fields and particles such as is needed to understand experiments carried out with the Large Hadron Collider at CERN. We are only going to need the basic mathematical tools of QFT in order to explore their application to some situations in social science. However, we will say a little about the very basic elements of the physical theory in order to set the scene and to point out what it is about them that makes them applicable to non-physical systems. But, it must be emphasized that it is not being suggested here that there is anything quantum mechanical, in the sense that physicists mean, in the social science cases that we are going to look at. That is, there are no quantum processes at the atomic level going on in the systems we are going to treat.^a

The situation is rather like the use of differential calculus. As we know, this was invented in C17 by Leibniz and Newton to address some problems in calculating the motion of material bodies. No one would now suggest that the calculus could not be applied to population growth or financial problems. Rates of change, which is what differential calculus deals with, are mathematically the same whether they are applied to planets or bank accounts. No one is arguing that the motion of the planets can affect your bank account! It is just that we are using the same mathematical tools to look at two entirely different phenomena. The same kind of argument is true for number operator algebra that was invented to do QFT, but which can also be used on bank accounts, and much more besides, as we shall see.

Finally, we remark that besides the purely mathematical elements of quantum theory, we shall explore the basics of quantum measurement theory, which is fundamentally based on the principle of complementarity, proposed by Niels Bohr. He argued that it is impossible to design a single measurement procedure that can provide complete information about the state of a quantum system. For example, for a quantum particle, we cannot measure both its position and momentum in the same experimental context. We can design either a measurement procedure for position or for momentum, but not for their joint measurement. It is worth pointing out that Bohr borrowed the principle of complementarity from psychology, see, e.g., [14]. Therefore, it is not surprising that this principle has to be taken into account...

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• Dedication
• Contents
• Preface
• About the Authors
• Part I Quantum Counting: The Number Operator in a Social Science Context
• Part II The Quantum-Like Paradigm with Simple Applications
• Part III The Quantum-Like Paradigm with Advanced Applications
• Index