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The main purpose of this volume is to emphasize the multidisciplinary aspects of this very active new line of research in which concrete technological and industrial realizations require the combined efforts of experimental and theoretical physicists, mathematicians and engineers.

Ohya, whose research interests include quantum entropy, quantum information theory, quantum computers, mathematical physics and information genetics, is the Dean of Science and Technology at the Tokyo U. of Science as well as the director and founder of university's Quantum Bio-Informatics Center. These 33 papers dating from the late 1970s to 2008 reflect his growth as a pioneer in rigorous, interdisciplinary study. For example, the most recent article in the collection addresses not only adaptive dynamics and its application to chaos but the thought of Sartre and Husserl.

This volume aims to return to the starting point of the fields of infinite dimensional analysis and quantum probability, fields that are growing rapidly at present, and to seriously attempt mutual interaction between the two, with a view to enumerating and solving the many fundamental problems they entail. For such a purpose, we look for interdisciplinary bridges in mathematics including classical probability and to different branches of physics, in particular, research for new paradigms for information science on the basis of quantum theory.