Structure of Dynamical Systems
Subtitle: A Symplectic View of Physics
By: by Jean-Marie Souriau
Series: Progress in Mathematics -- 149; Progress in Mathematics -- 149
Publisher: Birkhäuser Boston; Imprint: Birkhäuser
Published: 1997
Place of publication: Boston, MA
Language: eng
Format: [electronic resource] :
Number of pages: 406
ISBN-13: 9781461266921; 9781461202813
Subjects: Mathematics; Cell aggregation; Differentiable dynamical systems
Description: 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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