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Structure of Dynamical Systems: A Symplectic View of Physics (Progress in Mathematics) Hardcover – September 23, 1997

ISBN-13: 978-0817636951 ISBN-10: 0817636951 Edition: 1997th
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Editorial Reviews

Language Notes

Text: English (translation)
Original Language: French

From the Back Cover

This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization.

The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics.

The first tow chapters provide the necessary mathematical background in differential geometry, Lie groups, and symplectic geometry. In Chapter 3 a coherent symplectic description of Galilean and relativistic mechanics is given, culminating in the classification of elementary particles (relativistic and non-relativistic, with or without spin, with or without mass). In Chapter 4 statistical mechanics is put into symplectic form, finishing with a symplectic description of the kinetic theory of gases and the computation of specific heats. Finally, in Chapter 5 the author presents his theory of geometric quantization. Highlights of this chapter are the derivations of various wave equations and the construction of the Fock space.

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Product Details

  • Series: Progress in Mathematics (Book 149)
  • Hardcover: 406 pages
  • Publisher: Birkhäuser; 1997 edition (September 23, 1997)
  • Language: English
  • ISBN-10: 0817636951
  • ISBN-13: 978-0817636951
  • Product Dimensions: 6.1 x 1.1 x 9.2 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #1,081,406 in Books (See Top 100 in Books)

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12 of 13 people found the following review helpful By William Kirk on April 28, 2001
Format: Hardcover
The influence of this book is already large, and with this new edition of the English translation, destined to get bigger. Schlomo Sternberg at Harvard has already re-invented the way Undergrad Physics is usually taught with his Symplectic Approach, due in no small measure to his reading of this very book in its previous (French) incarnation. But Souriau is not only readable, and 'followable' in his expositions, the results are so delightful. The only complaint I would make is with the book editors' use of "cutesy" icons (spades, hearts, clubs, diamonds, something that looks like a bugle - for BIG results, one imagines hearing a fanfare every time one sees it), these sometimes get to be distracting. However, the editors' notes are useful and worthwhile. I fully believe the 'program' first enunciated (as far as I'm aware) in this book in 1968, will become more and more a dominant paradigm for physics in the 21st century.
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