A. Lichnerowicz – författare

Illustrates developments in the many areas of contemporary physics which have benefitted from the work and influence of Yvonne Choquet-Bruhat. The work considers the role of geometry of manifolds in space-time physics and that of functional analysis in quantum mechanics and quantum field theory.

This volume presents a unified theory of shock waves corresponding to gravitational and electromagnetic fields and to magnetohydrodynamics in the context of general relativity. The common tool employed is provided by tensor distribution - an approach which has been systematically developed by the author since 1962. One remarkable result is that this yields a complete theory of magnetohydrodynamic shock waves, which can also be applied to the treatment of pulsars. The same method is also applicable to the quantization of some physical fields in curved space-time. This, too, is discussed in the book. The text is suitable for graduate students and researchers in mathematical physics and theoretical astrophysics.

This volume presents a unified theory of shock waves corresponding to gravitational and electromagnetic fields and to magnetohydrodynamics in the context of general relativity. The common tool employed is provided by tensor distribution -- an approach which has been systematically developed by the author since 1962. One remarkable result is that this yields a complete theory of magnetohydrodynamic shock waves, which can also be applied to the treatment of pulsars. The same method is also applicable to the quantization of some physical fields in curved space-time. This, too, is discussed in the book. For graduate students and researchers in mathematical physics and theoretical astrophysics.

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.