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, K�hler 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.

Language Notes

Text: English (translation)
Original Language: German

"About this title" may belong to another edition of this title.

Store Description

Account dedicated to Print on Demand titles. Brook Bookstore offers a wide selection of books with a continuously updated catalog and fast shipments all over the world. We hold distribution rights with all of the publishers we promote and are in continuous search of new interesting titles to propose to our customers. We are part of Brandon Group SRL (an Italian company) and all of the orders are shipped from Europe. Depending on availability orders will be picked from our different warehouses. CONTACT US If you have any questions please do not hesitate to contact us sending a message to our store. We have a well prepared customer service team who will be happy to assist you. Our working hours are from Monday to Friday from 9:30 to 18:30 (CET, UTC +1) so messages received during the weekends might be responded with a slight delay but we guarantee you will get back to you as soon as possible. RETURNS If you want to return your order, please submit your request through Abebooks platform. Returns requests are managed case by case by our team and always in line with Abebooks policies: AbeBooks? Return Policy guarantees that you can return any book for a refund within 30 days, when the return is due to an error on the bookseller?s part. When the motive of the return is not due to an error of the seller it is up to Brook Bookstore to accept the return or else after studying the case. CANCELLATION You can send a cancellation request to our customer service team while the package has not yet been shipped. After that we cannot ensure we can retrieve the parcel but we suggest you to get in touch with us in order to verify the case. INVOICE You can request the invoice to be issued together with the shipment of the order or, at the latest, in the same month of the shipment.

Visit Seller's Storefront

Seller's business information

Brandon Group S.R.L.
Via Vannella Gaetani 27, Brandon Group, Napoli, NA, 80121, Italy

Sale & Shipping Terms

Terms of Sale

Account dedicated to Print on Demand titles.

CANCELLATION
You can send a cancellation request from the order page while the package has not yet been shipped. After that we cannot ensure we can retrieve the parcel but we suggest you to get in touch with us in order to verify the case.

INVOICE
You can request the invoice to be issued together with the shipment of the order or, at the latest, in the same month of the shipment.

RETURNS
If you want to return your order, please contact us for authoriz...

More Information

Shipping Terms

Shipping rates from Italy to U.S.A.

Shipping rates from Italy to U.S.A.
Order quantity	25 to 40 business days	60 to 60 business days
First item	US$ 7.85	US$ 589.87

Delivery times are set by sellers and vary by carrier and location. Orders passing through Customs may face delays and buyers are responsible for any associated duties or fees. Sellers may contact you regarding additional charges to cover any increased costs to ship your items.