Author | Souriau, Jean-Marie. author |
---|---|

Title | Structure of Dynamical Systems [electronic resource] : A Symplectic View of Physics / by Jean-Marie Souriau |

Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1997 |

Connect to | http://dx.doi.org/10.1007/978-1-4612-0281-3 |

Descript | XXXIV, 406 p. online resource |

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

CONTENT

I. Differential Geometry -- ยง1. Manifolds -- ยง2. Derivations -- ยง3. Differential equations -- ยง4. Differential forms -- ยง5. Foliated manifolds -- ยง6. Lie groups -- ยง7. The calculus of variations -- II. Symplectic Geometry -- ยง8. 2-Forms -- ยง9. Symplectic manifolds -- ยง10. Canonical transformations -- ยง11. Dynamical Groups -- III. Mechanics -- ยง12. The geometric structure of classical mechanics -- ยง13. The principles of symplectic mechanics -- ยง14. A mechanistic description of elementary particles -- ยง15. Particle dynamics -- IV. Statistical Mechanics -- ยง16. Measures on a manifold -- ยง17. The principles of statistical mechanics -- V. A Method of Quantization -- ยง18. Geometric quantization -- ยง19. Quantization of dynamical systems -- List of notation

Mathematics
Dynamics
Ergodic theory
Differential geometry
Manifolds (Mathematics)
Complex manifolds
Mathematics
Differential Geometry
Dynamical Systems and Ergodic Theory
Manifolds and Cell Complexes (incl. Diff.Topology)