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Ubiquitous quantum structure. From psychology to finance. (English) Zbl 1188.91002

Berlin: Springer (ISBN 978-3-642-05100-5/hbk; 978-3-642-05101-2/ebook). xiii, 216 p. (2010).
The reviewed book expounds a new “quantum-inspired” approach to mathematical modeling and draws attention to structural similarities in diverse fields. It is a rich source of ideas for further study. In this book quantum like structures are proposed to exist in diverse fields. Quantum like models, i.e., models based on the mathematical formalism of quantum mechanics and its generalizations can successfully be applied to cognitive science, psychology, genetics, economics, finance, and game theory.
Chapter one is an overview of the book’s contents. Chapter two gives a short review of quantum postulates and is therefore mainly of historical value: quantum mechanics is just the first example of the successful application of non-Kolmogorov probabilities, the first step towards a contextual probabilistic description of natural, biological, psychological, social, economical or financial phenomena. A general contextual probabilistic model (Vaxjo) is presented in chapter three. Chapter four shows that it can be used for describing probabilities in both quantum and classical (statistical) mechanics as well as in the phenomena mentioned above. This model can be represented in a quantum like way, namely, in complex and more general Hilbert spaces. In this way 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. Chapters 5 and 6 describe the brain as a quantum like model. Chapters 7, 8 and 9 describe game models as quantum like models. Chapters 10 and 11 describe financial models as quantum like models. This book is intended for psychologists and cognitive scientists.

MSC:

91-02 Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance
91B80 Applications of statistical and quantum mechanics to economics (econophysics)
91E10 Cognitive psychology
91A99 Game theory
91G99 Actuarial science and mathematical finance
81P99 Foundations, quantum information and its processing, quantum axioms, and philosophy
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