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008			081020s1997 maua |b 001 0 eng
010			_a97-000300
020			_a0817636951
020			_a3764336951
039		9	_a201402040051 _bVLOAD _c201008020848 _dmalmash _c200811111016 _dvenkatrajand _c200810201316 _dNoora _y200810201314 _zNoora
050	0	0	_aQC125.2 _b.S6813 1997
100	1		_aSouriau, J.-M. _q(Jean Marie), _d1922- _949028
245	1	0	_aStructure of Dynamical Systems : _bA Symplectic View of Physics / _cJ.-M. Souriau ; translated by C.H. Cushman-de Vries ; translation editors, R.H. Cushman, G.M. Tuynman.
260			_aBoston : _bBirkhauser, _cc1997.
300			_axxxiv, 406 p. : _bill. ; _c25 cm.
440		0	_aProgress in mathematics ; _vv. 149 _924858
504			_aIncludes bibliographical references (p. [387]-389) and index.
505			_aIntroduction.-Differential Geometry.-Manifolds.-Derivations.-Differential Equations.-Differential Forms.-Foliated Manifolds.-Lie Groups.-The Calculus of Variations.-Symplectic Geometry.-2-Forms.-Symplectic Manifolds.-Canonical Transformations.-Dynamical Groups.-Mechanics.-The Geometric Structure of Classical Mechanics.-The Principles of Symplectic Mechanics.-A Mechanistic Description of Elementary Particles.-Particles Dynamics.-Statistical Mechanics.-Measures on a Manifold.-The Principles of Statistical Mechanics.-A Method of Quantization.-Geometric Quantization.-Quantization of Dynamical Systems.-Bibliography.-Index.-List of Notation.
520			_aThis 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.
650		0	_aMechanics. _97171
650		0	_aStatistical mechanics. _94708
650		0	_aQuantum theory. _91606
650		0	_aSymplectic manifolds. _92646
650		0	_aMathematical physics. _9905
942			_2lcc _n0 _cBK
999			_c23124 _d23124