Symplectic Geometry and Mathematical Physics: Actes Du Colloque en L'honneur de Jean-Marie Souriau ; [ Conference Held in Aix-en-Provence (France), June 11 - 15, 1990]P. Donato Springer Science & Business Media, 1991 - 478 strani 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. |
Vsebina
Some Remarks on Quantization | 37 |
The Variety of all Invariant Symplectic Structures on | 80 |
On Singular Reduction of Hamiltonian Spaces | 114 |
Formes normales de Structures de Poisson | 129 |
An Exterior Differential Systems Approach to the Cartan Form | 160 |
The Rotor and the Pendulum | 189 |
On the Quantization of Poisson Algebras | 204 |
Simple Quantization Formula | 234 |
Heisenberg and Isoholonomic Inequalities | 303 |
Internal Supersymmetry and Superconnections | 326 |
Quelques remarques sur les variétés de PoissonNijenhuis | 355 |
Algèbres de Lie graduées et quantification | 374 |
An Analogue of B G G Resolution for the Quantum SLNGroup | 422 |
Orbites coadjointes et caractères | 442 |
Reduction Procedures for Poisson Manifolds | 462 |
List of Participants | 477 |
Géométrie des systèmes mécaniques à liaisons actives | 260 |
Structures de Poisson affines | 288 |
Druge izdaje - Prikaži vse
Symplectic Geometry and Mathematical Physics: Actes Du Colloque en L'honneur ... Paul Donato Prikaz kratkega opisa - 1991 |
Pogosti izrazi in povedi
action affine algèbre de Lie associated bigèbre bracket bundle canonical Cartan form Cent gx champ de vecteurs classical Lepagean equivalent coadjoint orbit cohomologie commutative complex convexity coordonnées locales corresponding crochet d'une decomposition defined définie déformation denote differential élément equations example formula geodesic geometric quantization groupe kählérien groupoid Hamiltonian integral invariant invariante à gauche isomorphism Jacobi Jean-Marie Souriau Kähler Kähler manifold Killing tensors Kostant l'algèbre Lagrangian liaisons Lie algebra Lie graduée Lie group linear Math matrix metric momentum map morphism Nijenhuis nilpotent opérateur orthogonal peut Poincaré-Cartan form Poisson algebra Poisson bracket Poisson manifold Poisson structure polarization projection Proof Proposition quantum reduced space representation Riemannian semisimple smooth function Souriau sous-algèbre structure de Poisson subalgebra submanifold Symp symplectic manifold symplectique tangent tenseur Theorem théorème theory Toda lattice tout variables variational problem variété vector fields vérifie Weinstein