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)

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
Creator
Author
Author
Subject
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 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
Member of
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
QA641-670
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)
Instantiates
Publication
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. 2-Forms -- §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
10.1007/978-1-4612-0281-3
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
  • (DE-He213)978-1-4612-0281-3
  • (MiAaPQ)EBC3074311
  • (EXLCZ)993400000000089066
Label
Structure of Dynamical Systems : A Symplectic View of Physics, by J.M. Souriau, (electronic resource)
Publication
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. 2-Forms -- §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
10.1007/978-1-4612-0281-3
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
  • (DE-He213)978-1-4612-0281-3
  • (MiAaPQ)EBC3074311
  • (EXLCZ)993400000000089066

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