The Classical Dynamics of Particles

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

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

5.2. Wigner-Van Dam Theory (Two-Body Motion when m2>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