M. Flato

R. Kerner

A. Lichnerowicz

This volume contains the proceedings of the Colloquium "Analysis, Manifolds and Physics" organized in honour of Yvonne Choquet-Bruhat by her friends, collaborators and former students, on June 3, 4 and 5, 1992 in Paris. Its title accurately reflects the domains to which Yvonne Choquet-Bruhat has made essential contributions. Since the rise of General Relativity, the geometry of Manifolds has become a non-trivial part of space-time physics. At the same time, Functional Analysis has been of enormous importance in Quantum Mechanics, and Quantum Field Theory. Its role becomes decisive when one considers the global behaviour of solutions of differential systems on manifolds. In this sense, General Relativity is an exceptional theory in which the solutions of a highly non-linear system of partial differential equations define by themselves the very manifold on which they are supposed to exist. This is why a solution of Einstein's equations cannot be physically interpreted before its global behaviour is known, taking into account the entire hypothetical underlying manifold. In her youth, Yvonne Choquet-Bruhat contributed in a spectacular way to this domain stretching between physics and mathematics, when she gave the proof of the existence of solutions to Einstein's equations on differential manifolds of a quite general type. The methods she created have been worked out by the French school of mathematics, principally by Jean Leray. Her first proof of the local existence and uniqueness of solutions of Einstein's equations inspired Jean Leray's theory of general hyperbolic systems.

Proceedings of the International Colloquium in honour of Yvonne Choquet-Bruhat, Paris, June 3–5, 1992

Physics on Manifolds

J.P. Vigier

Z. Maric

A. Milojevic

Daniel Sternheimer

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

M. Cahen

On the occasion of the sixtieth birthday of Andre Lichnerowicz a number of his friends, many of whom have been his students or coworkers, decided to celebrate this event by preparing a jubilee volume of contributed articles in the two main fields of research marked by Lichnerowicz's work, namely differential geometry and mathematical physics. Limitations of space and time did not enable us to include papers from all Lichnerowicz's friends nor from all his former students. It was equally impossible to reflect in a single book the great variety of subjects tackled by Lichnerowicz. In spite of these limitations, we hope that this book reflects some of the present trends of fields in which he worked, and some of the subjects to which he contributed in his long - and not yet finished - career. This career was very much marked by the influence of his masters, Elie Cartan who introduced him to research in mathematics, mainly in geometry and its relations with mathematical physics, and Georges Darmois who developed his interest for mechanics and physics, especially the theory of relativity and electromagnetism. This par ticular combination, and his personal talent, made of him a natural scientific heir and continuator of the French mathematical physics school in the tradition of Henri Poincare. Some of his works would even be best qualified by a new field name, that of physical ma thematics: branches of pure mathematics entirely motivated by physics.

A Volume in Honour of André Lichnerowicz on His 60th Birthday

Differential Geometry and Relativity

M. Flato

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