Ubiquitous Quantum Structure

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, economics, finances, and game theory.

This book is not about quantum mechanics as a physical theory. The short review of quantum postulates 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 (Växjö model) is presented. It can be used for describing probabilities in both quantum and classical (statistical) mechanics as well as in the above mentioned phenomena. 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.

Professor Khrennikov works actively in quantum foundations concentrating his research on such fundamental problems as inter-relation of quantum and classical probability, quantum nonlocality, Bell's inequality, interference of probabilities. He was one of the first in the world who started to apply quantum mathematics outside physics - in psychology, cognitive science, genetics, economy and finances. He published about 300 papers in the most prestigious journals in physics, mathematics, biology, psychology, finances, cognitive science. He is the author of 11 monographs on foundations of probability, quantum physics, p-adic and non-Archimedean analysis and their applications. Since 2001, Prof. Khrennikov is the director of The International Center for Mathematical Modeling in Physics and Cognitive Science, University of Vaxjo Sweden. This center has already organized 10 conferences on foundations of probability and quantum physics, workshops on quantum psychology and quantum finances.