An Introduction to Symplectic Geometry (Graduate Studies in Mathematics) (Graduate Studies in Mathematics),Used

An Introduction to Symplectic Geometry (Graduate Studies in Mathematics) (Graduate Studies in Mathematics),Used

In Stock
SKU: SONG0821820567
Brand: Brand: American Mathematical Society
$71.70 $102.43
Save $30.73
Quantity
Add to wishlist
Add to compare

Processing time: 1-3 days

US Orders Ships in: 3-5 days

International Orders Ships in: 8-12 days

Return Policy: 15-days return on defective items

Payment Option
Payment Methods

Help

If you have any questions, you are always welcome to contact us. We'll get back to you as soon as possible, withing 24 hours on weekdays.

Customer service

All questions about your order, return and delivery must be sent to our customer service team by e-mail at yourstore@yourdomain.com

Sale & Press

If you are interested in selling our products, need more information about our brand or wish to make a collaboration, please contact us at press@yourdomain.com

Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored. In addition to the essential classic results, such as Darboux's theorem, more recent results and ideas are also included here, such as symplectic capacity and pseudoholomorphic curves. These ideas have revolutionized the subject. The main examples of symplectic manifolds are given, including the cotangent bundle, Khler manifolds, and coadjoint orbits. Further principal ideas are carefully examined, such as Hamiltonian vector fields, the Poisson bracket, and connections with contact manifolds. Berndt describes some of the close connections between symplectic geometry and mathematical physics in the last two chapters of the book. In particular, the moment map is defined and explored, both mathematically and in its relation to physics. He also introduces symplectic reduction, which is an important tool for reducing the number of variables in a physical system and for constructing new symplectic manifolds from old. The final chapter is on quantization, which uses symplectic methods to take classical mechanics to quantum mechanics. This section includes a discussion of the Heisenberg group and the Weil (or metaplectic) representation of the symplectic group. Several appendices provide background material on vector bundles, on cohomology, and on Lie groups and Lie algebras and their representations. Berndt's presentation of symplectic geometry is a clear and concise introduction to the major methods and applications of the subject, and requires only a minimum of prerequisites. This book would be an excellent text for a graduate course or as a source for anyone who wishes to learn about symplectic geometry.

⚠️ WARNING (California Proposition 65):

This product may contain chemicals known to the State of California to cause cancer, birth defects, or other reproductive harm.

For more information, please visit www.P65Warnings.ca.gov.

Recently Viewed