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Structure of Dynamical Systems: A Symplectic View of Physics: 149 (Progress in Mathematics, 149) - Hardcover
Synopsis
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. 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.
"synopsis" may belong to another edition of this title.
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.
Synopsis
The aim of this text is to treat all three basic theories of physics (classical, statistical and quantum mechanics) from the same perspective, namely that of symplectic geometry, in order to show the unifing power of the symplectic geometry approach. The book aims to give the reader an understanding of the interrelationships of the three basic theories of physics. The first two chapters give the necessary mathematical background in differential geometry, Lie groups, and symplectic geometry. In chapter three a 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 the fourth chapter statistic mechanics is put into symplectic form, finishing with a symplectic description of the kinetic theory of gases and the computation of specific heats. The final chapter covers the author's theory of geometric quantization, and included in this chapter are the derivations of the various wave equations, and the construction of the Fock space.
This text is aimed at graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics and geometric quantization."About this title" may belong to another edition of this title.
- Publication date1703
- ISBN 10 0817636951
- ISBN 13 9780817636951
- BindingHardcover
- LanguageEnglish
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