Ubiquitous Quantum Structure From Psychology to Finance
Quantum-like structure is present practically everywhere. Quantum-like (QL) models, i.e. models based on the mathematical formalism of quantum mechanics and its generalizations can be successfully applied to cognitive science, psychology, genetics, e
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Ubiquitous Quantum Structure From Psychology to Finance
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Ubiquitous Quantum Structure
Andrei Khrennikov
Ubiquitous Quantum Structure From Psychology to Finance
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Prof. Andrei Khrennikov University of V¨axj¨o International Center for Mathematical Modeling in Physics and Cognitive Science Vejdes Plats 7 SE-351 95 V¨axj¨o Sweden [email protected]
ISBN 978-3-642-05100-5 e-ISBN 978-3-642-05101-2 DOI 10.1007/978-3-642-05101-2 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2009943303 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik, Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The aim of this book is to demonstrate that quantum-like (QL) models, i.e., models based on the mathematical formalism of quantum mechanics (QM) and its generalizations, can be successfully applied to cognitive science, psychology, genetics, the economy, finances, and game theory. This book is not about quantum mechanics as a physical theory. The short review of quantum postulates has merely historical value: quantum mechanics is just the first example of successful application of non-Kolmogorovian probabilities, the first step towards a contextual probabilistic description of natural, biological, psychological, social, economic or financial phenomena. I have developed a general contextual probabilistic model (V¨axj¨o model) that can be used to describe probabilities in both quantum and classical (statistical) mechanics as well as in the above-mentioned phenomena. This model can be represented in a QL way, namely, in complex and more general Hilbert spaces. In particular, quantum probability is totally demystified: Born’s representation of quantum probabilities by complex probability amplitudes, wave functions, is simply a special representation of this type. QL representation of data is very convenient; it can be used in any domain of science. I have presented [180, 198] a fundamental conjecture that some biological systems might develop the ability to create QL representations of external and internal worlds. Starting with this conjecture, QL models of cognitive and psycho
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