This volume contains the proceedings of the conference "Colloque de Goometrie Symplectique et Physique Mathematique" which was held in Aix-en-Provence (France), June 11-15, 1990, in honor of Jean-Marie Souriau. The conference was one in the series of international meetings of the Seminaire Sud Rhodanien de Goometrie, an organization of geometers and mathematical physicists at the Universities of Avignon, Lyon, Mar seille, and Montpellier. The scientific interests of Souriau, one of the founders of geometric quantization, range from classical mechanics (symplectic geometry) and quantization problems to general relativity and astrophysics. The themes of this conference cover "only" the first two of these four areas. The subjects treated in this volume could be classified in the follow ing way: symplectic and Poisson geometry (Arms-Wilbour, Bloch-Ratiu, Brylinski-Kostant, Cushman-Sjamaar, Dufour, Lichnerowicz, Medina, Ouzilou), classical mechanics (Benenti, Holm-Marsden, Marle) , particles and fields in physics (Garcia Perez-Munoz Masque, Gotay, Montgomery, Ne'eman-Sternberg, Sniatycki) and quantization (Blattner, Huebschmann, Karasev, Rawnsley, Roger, Rosso, Weinstein). However, these subjects are so interrelated that a classification by headings such as "pure differential geometry, applications of Lie groups, constrained systems in physics, etc. ," would have produced a completely different clustering! The list of authors is not quite identical to the list of speakers at the conference. M. Karasev was invited but unable to attend; C. Itzykson and M. Vergne spoke on work which is represented here only by the title of Itzykson's talk (Surfaces triangulees et integration matricielle) and a summary of Vergne's talk.
Reihe
Auflage
Softcover reprint of the original 1st ed. 1991
Sprache
Verlagsort
Verlagsgruppe
Maße
Höhe: 23.5 cm
Breite: 15.5 cm
ISBN-13
978-1-4757-2141-6 (9781475721416)
DOI
10.1007/978-1-4757-2140-9
Schweitzer Klassifikation
Separation of Variables in the Geodesic Hamilton-Jacobi Equation.- Some Remarks on Quantization.- Convexity and Integrability.- The Variety of all Invariant Symplectic Structures on a Homogeneous Space and Normalizers of Isotropy Subgroups.- On Singular Reduction of Hamiltonian Spaces.- Formes normales de Structures de Poisson.- Higher Order Regular Variational Problems.- An Exterior Differential Systems Approach to the Cartan Form.- The Rotor and the Pendulum.- On the Quantization of Poisson Algebras.- Simple Quantization Formula.- Les groupes kählériens.- Géométrie des systèmes mécaniques à liaisons actives.- Structures de Poisson affines.- Heisenberg and Isoholonomic Inequalities.- Internal Supersymmetry and Superconnections.- Quelques remarques sur les variétés de Poisson-Nijenhuis.- Deformation quantization of Kähler manifolds.- Algèbres de Lie graduées et quantification.- An Analogue of B.G.G. Resolution for the Quantum SL(N)-Group.- Hamiltonian Constraints, the Jacobi Principle and Gravity.- Orbites coadjointes et caractères.- Noncommutative Geometry and Geometric Quantization.- Reduction Procedures for Poisson Manifolds.- List of Participants.