Yoshiaki Maeda

Daniel Sternheimer

Hideki Omori

Hitoshi Moriyoshi

Tatsuya Tate

Satoshi Watamura

Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments. However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation problems, Poisson groupoids, operad theory, quantization problems, and D-branes. The meeting was attended by both mathematicians and physicists, which resulted in interesting discussions. This volume contains the refereed proceedings of this symposium. Providing a state of the art overview of research in these topics, this book is suitable as a source book for a seminar in noncommutative geometry and physics.

Proceedings of the Workshop at Shonan, Japan, June 1999

Noncommutative Differential Geometry and Its Applications to Physics

J.P. Vigier

M. Flato

Z. Maric

A. Milojevic

Two important events in the history of physical sciences occurred re cently: the fiftieth anniversary of Quantum Mechanics and the Jubilee of Louis de Broglie's celebrated Thesis. These events occurred in the same period of time when the world honored de Broglie on the occa sion of his eightieth birthday. Some of de Broglie's friends, former students, and some people who used to know him and appreciate his personality decided to prepare an international volume for this cele brated occasion. Such a task was not very easy. It is always simpler to contribute in honor of famous people whose works and impact were great on a tech nical and pragmatic level than to contribute in honor of a person whose achievements were not only dominant in physical sciences themselves, but also had many important implications for the development of the whole branch of philosophy of sciences. Louis de Broglie, the man to whom we owe among other things the most fundamental notion of duality between waves and particles, be longs in a way to the Einsteinian school of thought. He never accepted literally the Copenhagen interpretation of quantum mechanics. To him it was clear that this interpretation makes quantum mechanics incomplete and highly non-deterministic. He always believed that since the duality between waves and particles was an experimental fact, there should be some manifestation of the Schrodinger wave itself in the realistic world. De Broglie had to struggle much for this idea, which he never gave up.

An International Collection of Contributions in Honor of Louis de Broglie on the Occasion of the Jubilee of His Celebrated Thesis

Quantum Mechanics, Determinism, Causality, and Particles

Daniel Sternheimer

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