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.
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and ...
This book would be an excellent text for a graduate course or as a source for anyone who wishes to learn about symplectic geometry.
This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds.
Our proof makes use of the transitivity of the action of Sp(2n,R) on the Lagrangian Grassmannian Lag(2n,R). Theorem 60. For every S ∈ Sp(2n,R) there exist two ... for given l, choose l transversal to both lP and Sl: l∩lP=l∩Sl={0}.
This volume contains papers presented at the meeting Deformation Theory, Symplectic Geometry and Applications, held in Ascona, June 17-21, 1996. The contents touch upon many frontier domains of modern...
This introductory book offers a unique and unified overview of symplectic geometry, highlighting the differential properties of symplectic manifolds.
This work can be used as a textbook for graduate courses, but the depth of coverage and the wealth of information and application means that it will be of continuing interest to, and of lasting significance for mathematicians and ...
This book offers a complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics.
The second of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1).
This volume presents lectures given at the Wisła 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisła, Poland, and was organized by the Baltic ...