The Classical Dynamics of Particles: Galilean and Lorentz Relativity has been designed to serve either as an independent graduate course in dynamics or as a segment of a graduate theoretical physics course. The book begins with a general introduction and a rather extensive discussion of the special theory of relativity, including a section on tachyons. Separate chapters follow on the variational derivation of Lagrangian dynamical equations of charged particle motion and spin angular momentum; variational derivation of Noether's theorem; and canonical formalism and Dirac's extension of Hamiltonian dynamics and treatment of constraints. The ""No-Interaction Theorem"" of Wigner and Van Dam and various efforts to construct a many-particle dynamics compatible with the special theory of relativity are also discussed. The final chapter presents two applications of group theory in classical mechanics: the factorization of the dynamical matrix and the construction of a canonical formalism from a symmetry group.
This text is intended for advanced undergraduate or graduate students of physics. It is assumed that the reader has had an undergraduate course in mechanics and the usual undergraduate mathematics preparation including differential equations and matrix theory. Some exposure to elementary tensors and group theory would be helpful but is not essential

Contenu

Preface
1 Classical Dynamics of Particles
1.1. Preliminary Concepts
1.2. Salient Features of the Special Theory of Relativity
1.3. Solved Examples
Problems
References
Bibliography
2 Lagrangian Dynamics
2.1. Basic Theory
2.2. Development and Extension of the Basic Theory
2.3. Solved Examples
Problems
References
Bibliography
3 Conservation Laws
3.1. Relationship of Conservation Laws and Symmetry Transformations
3.2. Conservation Laws Associated with Lorentz Transformations
3.3. Solved Examples
Problems
References
Bibliography
4 The Canonical Formalism
4.1. Basic Theory
4.2. Development and Extension of the Basic Theory
4.3. Solved Examples
Problems
References
Bibliography
5 Many-Particle Dynamics
5.1. Construction of a Many-Particle Dynamics Compatible with Einstein's Special Theory of Relativity
>m1)
References
6 Group Theory
6.1. Group Theory in Classical Mechanics
6.2. Factoring the Dynamical Matrix
6.3. Constructing a Canonical Formalism from a Symmetry Group
Problems
References
Appendix A Some Useful Mathematics
Appendix B Derivation of Lagrange's Equations from Newton's Laws
Appendix C Leutwyler's Proof of the No-Interaction Theorem
Appendix D Euler Angles
Appendix E Some Group Theory
Appendix F Point Groups and Their Character Tables
Index