Physics on Manifolds: Proceedings of the International Colloquium in Honour of Yvonne Choquet-Bruhat, Paris, June 3-5, 1992

ISBN-13: 9789401048576 / Angielski / Miękka / 2012 / 366 str.

M. Flato; R. Kerner; A. Lichnerowicz

Opis

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.

Spis treści

Foreword. Introduction; J.C. Legrand. Relativistic dissipative fluids; A.M. Anile, G. Ali, V. Romano. Mathematical problems related to liquid crystals, superconductors and superfluids; H. Brezis. Microcanonical action and the entropy of a rotating black hole; J.D. Brown, J.W. York, Jr. Problème de Cauchy sur un cônoïde caractéristique. Applications à certains systèmes non linéaires d'origine physique; F. Cagnac, M. Dossa. Recent progress on the Cauchy problem in general relativity; D. Christodoulou. On some links between mathematical physics and physics in the context of general relativity; T. Damour. Functional integration. A multipurpose tool; C. DeWitt-Morette. Generalized frames of references and intrinsic Cauchy problem in general relativity; G. Ferrarese, C. Cattani. Reducing Einstein's equations to an unconstrained hamiltonian system on the cotangent bundle of Teichmüller space; A.E. Fischer, V. Moncrief. Darboux transformations for a class of integrable systems in n variables; C.H. Gu. Group theoretical treatment of fundamental solutions; N.H. Ibragimov. On the regularity properties of the wave equation; S. Klainerman, M. Machedon. Le problème de Cauchy linéaire et analytique pour un opérateur holomorphe et un second membre ramifié; J. Leray. On Boltzmann equation; P.L. Lions. Star products and quantum groups; C. Moreno, L. Valero. On asymptotic of solutions of a nonlinear elliptic equation in a cylindrical domain; O. Oleinik. Fundamental physics in universal space-time; I. Segal. Interaction of gravitational and electromagnetic waves in general relativity; A.H. Taub. Anti-self dual conformal structures on 4-manifolds; C. Taubes. Chaotic behavior inrelativistic motion; E. Calzetta. Some results on non constant mean curvature solutions of the Einstein constraint equations; J. Isenberg, V. Moncrief. Levi condition for general systems; W. Matsumoto. Conditions invariantes pour un système, du type conditions de Levi; J. Vaillant. Black holes in supergravity; P.C. Aichelburg. Low-dimensional behaviour in the rotating driven cavity problem; E.A. Christensen, J.N. Sorensen, M. Brons, P.L. Christiansen. Some geometrical aspects of inhomogeneous elasticity; M. Epstein, G.A. Maugin. Integrating the Kadomtsev-Petviashvili equation in the 1+3 dimensions via the generalised Monge-Ampère equation: an example of conditioned Painlevé test; T. Brugarino, A. Greco. Spinning mass endowed with electric charge and magnetic dipole moment; V.S. Manko, N.R. Sibgatullin. Equations de Vlasov en théorie discrète; G. Pichon. Convexity and symmetrization in classical and relativistic balance laws systems; T. Ruggeri.