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One of the most enduring elements in theoretical physics has been
group theory. GROUP 24: Physical and Mathematical Aspects of
Symmetries provides an important selection of informative articles
describing recent advances in the field. The applications of group
theory presented in this book deal not only with the traditional
fields of physics, but also include such disciplines as chemistry
and biology.
Awarded the Wigner Medal and the Weyl Prize, respectively, H.J.
Lipkin and E. Frenkel begin the volume with their contributions.
Plenary session contributions are represented by 18 longer
articles, followed by nearly 200 shorter articles. The book also
presents coherent states, wavelets, and applications and quantum
group theory and integrable systems in two separate sections.
As a record of an international meeting devoted to the physical and
mathematical aspects of group theory, GROUP 24: Physical and
Mathematical Aspects of Symmetries constitutes an essential
reference for all researchers interested in various current
developments related to the important concept of symmetry.
One of the most enduring elements in theoretical physics has been
group theory. GROUP 24: Physical and Mathematical Aspects of
Symmetries provides an important selection of informative articles
describing recent advances in the field. The applications of group
theory presented in this book deal not only with the traditional
fields of physics, but also include such disciplines as chemistry
and biology.Awarded the Wigner Medal and the Weyl Prize,
respectively, H.J. Lipkin and E. Frenkel begin the volume with
their contributions. Plenary session contributions are represented
by 18 longer articles, followed by nearly 200 shorter articles. The
book also presents coherent states, wavelets, and applications and
quantum group theory and integrable systems in two separate
sections.As a record of an international meeting devoted to the
physical and mathematical aspects of group theory, GROUP 24:
Physical and Mathematical Aspects of Symmetries constitutes an
essential reference for all researchers interested in various
current developments related to the important concept of symmetry.
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.
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. Probleme de Cauchy sur un conoide
caracteristique. Applications a certains systemes non lineaires
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
Teichmuller 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 probleme de Cauchy lineaire et
analytique pour un operateur holomorphe et un second membre
ramifie; 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 systeme, 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-Ampere equation: an example of conditioned
Painleve 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 theorie discrete; G. Pichon.
Convexity and symmetrization in classical and relativistic balance
laws systems; T. Ruggeri.
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