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The Resource Structure of Dynamical Systems : A Symplectic View of Physics, by J.M. Souriau, (electronic resource)
Structure of Dynamical Systems : A Symplectic View of Physics, by J.M. Souriau, (electronic resource)
Resource Information
The item Structure of Dynamical Systems : A Symplectic View of Physics, by J.M. Souriau, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Structure of Dynamical Systems : A Symplectic View of Physics, by J.M. Souriau, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 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 nonrelativistic, 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
 Language

 eng
 eng
 Edition
 1st ed. 1997.
 Extent
 1 online resource (XXXIV, 406 p.)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Contents

 I. Differential Geometry
 §1. Manifolds
 §2. Derivations
 §3. Differential equations
 §4. Differential forms
 §5. Foliated manifolds
 §6. Lie groups
 §7. The calculus of variations
 II. Symplectic Geometry
 §8. 2Forms
 §9. Symplectic manifolds
 §10. Canonical transformations
 §11. Dynamical Groups
 III. Mechanics
 §12. The geometric structure of classical mechanics
 §13. The principles of symplectic mechanics
 §14. A mechanistic description of elementary particles
 §15. Particle dynamics
 IV. Statistical Mechanics
 §16. Measures on a manifold
 §17. The principles of statistical mechanics
 V. A Method of Quantization
 §18. Geometric quantization
 §19. Quantization of dynamical systems
 List of notation
 Isbn
 9781461202813
 Label
 Structure of Dynamical Systems : A Symplectic View of Physics
 Title
 Structure of Dynamical Systems
 Title remainder
 A Symplectic View of Physics
 Statement of responsibility
 by J.M. Souriau
 Language

 eng
 eng
 Summary
 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 nonrelativistic, 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
 http://library.link/vocab/creatorName
 Souriau, J.M
 Dewey number
 516.36
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 kRjAEH_P230
 Image bit depth
 0
 Language note
 English
 LC call number
 QA641670
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement
 Progress in Mathematics,
 Series volume
 149
 http://library.link/vocab/subjectName

 Global differential geometry
 Differentiable dynamical systems
 Cell aggregation
 Differential Geometry
 Dynamical Systems and Ergodic Theory
 Manifolds and Cell Complexes (incl. Diff.Topology)
 Label
 Structure of Dynamical Systems : A Symplectic View of Physics, by J.M. Souriau, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Contents
 I. Differential Geometry  §1. Manifolds  §2. Derivations  §3. Differential equations  §4. Differential forms  §5. Foliated manifolds  §6. Lie groups  §7. The calculus of variations  II. Symplectic Geometry  §8. 2Forms  §9. Symplectic manifolds  §10. Canonical transformations  §11. Dynamical Groups  III. Mechanics  §12. The geometric structure of classical mechanics  §13. The principles of symplectic mechanics  §14. A mechanistic description of elementary particles  §15. Particle dynamics  IV. Statistical Mechanics  §16. Measures on a manifold  §17. The principles of statistical mechanics  V. A Method of Quantization  §18. Geometric quantization  §19. Quantization of dynamical systems  List of notation
 Dimensions
 unknown
 Edition
 1st ed. 1997.
 Extent
 1 online resource (XXXIV, 406 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781461202813
 Level of compression
 uncompressed
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781461202813
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3400000000089066
 (SSID)ssj0001298638
 (PQKBManifestationID)11724920
 (PQKBTitleCode)TC0001298638
 (PQKBWorkID)11242310
 (PQKB)11410423
 (DEHe213)9781461202813
 (MiAaPQ)EBC3074311
 (EXLCZ)993400000000089066
 Label
 Structure of Dynamical Systems : A Symplectic View of Physics, by J.M. Souriau, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Contents
 I. Differential Geometry  §1. Manifolds  §2. Derivations  §3. Differential equations  §4. Differential forms  §5. Foliated manifolds  §6. Lie groups  §7. The calculus of variations  II. Symplectic Geometry  §8. 2Forms  §9. Symplectic manifolds  §10. Canonical transformations  §11. Dynamical Groups  III. Mechanics  §12. The geometric structure of classical mechanics  §13. The principles of symplectic mechanics  §14. A mechanistic description of elementary particles  §15. Particle dynamics  IV. Statistical Mechanics  §16. Measures on a manifold  §17. The principles of statistical mechanics  V. A Method of Quantization  §18. Geometric quantization  §19. Quantization of dynamical systems  List of notation
 Dimensions
 unknown
 Edition
 1st ed. 1997.
 Extent
 1 online resource (XXXIV, 406 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781461202813
 Level of compression
 uncompressed
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781461202813
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3400000000089066
 (SSID)ssj0001298638
 (PQKBManifestationID)11724920
 (PQKBTitleCode)TC0001298638
 (PQKBWorkID)11242310
 (PQKB)11410423
 (DEHe213)9781461202813
 (MiAaPQ)EBC3074311
 (EXLCZ)993400000000089066
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