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Progress in Mathematics

Structure of Dynamical Systems

A Symplectic View of Physics

Authors: Souriau, J.M.

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About this book

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.

Table of contents (19 chapters)

Table of contents (19 chapters)

Buy this book

eBook $119.00
price for USA in USD
  • ISBN 978-1-4612-0281-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $249.99
price for USA in USD
  • ISBN 978-0-8176-3695-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $159.99
price for USA in USD
  • ISBN 978-1-4612-6692-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Structure of Dynamical Systems
Book Subtitle
A Symplectic View of Physics
Authors
Series Title
Progress in Mathematics
Series Volume
149
Copyright
1997
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0281-3
DOI
10.1007/978-1-4612-0281-3
Hardcover ISBN
978-0-8176-3695-1
Softcover ISBN
978-1-4612-6692-1
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XXXIV, 406
Topics