Table of contents
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.
- Book Title Structure of Dynamical Systems
- Book Subtitle A Symplectic View of Physics
- Series Title Progress in Mathematics
- Series Abbreviated Title Progress in Mathematics(Birkhäuser)
- DOI https://doi.org/10.1007/978-1-4612-0281-3
- Copyright Information Birkhäuser Boston 1997
- Publisher Name Birkhäuser, Boston, MA
- eBook Packages Springer Book Archive
- Hardcover ISBN 978-0-8176-3695-1
- Softcover ISBN 978-1-4612-6692-1
- eBook ISBN 978-1-4612-0281-3
- Series ISSN 0743-1643
- Series E-ISSN 2296-505X
- Edition Number 1
- Number of Pages XXXIV, 406
- Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
Dynamical Systems and Ergodic Theory
Manifolds and Cell Complexes (incl. Diff.Topology)
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