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© 1997

Structure of Dynamical Systems

A Symplectic View of Physics

Book

Part of the Progress in Mathematics book series (PM, volume 149)

Table of contents

  1. Front Matter
    Pages i-xxxiv
  2. Differential Geometry

    1. Front Matter
      Pages 1-1
    2. Jean-Marie Souriau
      Pages 3-17
    3. Jean-Marie Souriau
      Pages 18-26
    4. Jean-Marie Souriau
      Pages 27-30
    5. Jean-Marie Souriau
      Pages 31-37
    6. Jean-Marie Souriau
      Pages 38-44
    7. Jean-Marie Souriau
      Pages 45-61
    8. Jean-Marie Souriau
      Pages 62-69
  3. Symplectic Geometry

    1. Front Matter
      Pages 71-71
    2. Jean-Marie Souriau
      Pages 73-80
    3. Jean-Marie Souriau
      Pages 81-89
    4. Jean-Marie Souriau
      Pages 90-99
    5. Jean-Marie Souriau
      Pages 100-117
  4. Mechanics

    1. Front Matter
      Pages 119-119
    2. Jean-Marie Souriau
      Pages 121-153
    3. Jean-Marie Souriau
      Pages 154-172
    4. Jean-Marie Souriau
      Pages 173-193
    5. Jean-Marie Souriau
      Pages 194-219
  5. Statistical Mechanics

    1. Front Matter
      Pages 221-221

About this book

Introduction

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.

Keywords

Derivation calculus differential geometry equation geometry manifold mathematics quantum mechanics symplectic geometry

Authors and affiliations

  1. 1.UFR de MathématiquesUniversité de ProvenceMarseilleFrance

Bibliographic information