Book Review: “Introduction to the Classical Theory of Particles and Fields”, by Boris Kosyakov. Springer, Heidelberg 2007, ISBN: 978-3-540-40933-5, 493 pages, 34 figures, ca. EUR 140,–
✍ Scribed by Y.N. Obukhov
- Book ID
- 101483182
- Publisher
- John Wiley and Sons
- Year
- 2007
- Tongue
- English
- Weight
- 81 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0003-3804
No coin nor oath required. For personal study only.
✦ Synopsis
The classical theory of gauge fields is an important subject that has numerous applications in modern physics. Courses on classical Maxwell-Lorentz electrodynamics are necessarily included in the programs of all physics and engineering departments of universities. In this sense, the new book is addressed to a very wide audience. It is, however, not a textbook that covers all the aspects of electrodynamics. The author confines his attention mainly to the dynamics of the coupled system of the electric and magnetic fields and the charged point particles in vacuum. In the choice of the subject, the book is thus very similar to the wellknown monograph of F. Rohrlich, "Classical charged particles" (3rd ed., World Scientific, Singapore 2007). Moreover, the author explicitly mentions that his idea was to give a new account of the old self-interaction problem that was in the center of Rohrlich's book. In my view, this task was successfully fulfilled and the author presented a nice unified picture that describes the dynamics of classical particles with Abelian and non-Abelian charges in electrodynamical and in Yang-Mills fields.
A nice feature of this book is that it is self-contained. All the necessary definitions as well as the technical tools are provided by the author in the main body of the book. In addition, six appendices collect the basic facts about differential forms, Lie groups and algebras, spinors, and distributions. Accordingly, a serious student can learn the subject step by step, without using other sources. Moreover, the numerous exercises (all together more than 250) are scattered over the text, and this definitely brings this volume closer to a textbook useful for classroom work rather than being a pure monograph.
The structure of the book seems to be well thought out. Chaps. 1-3 can be considered as a general background of the picture drawn by the author. The first chapter introduces the reader to the geometry of Minkowski spacetime. The points, vectors, tensors, forms, affine and metric structures are explained here in sufficient detail. The Chap. 2 presents the relativistic mechanics of structureless point particles in Minkowski spacetime. The Lagrangian formulation is developed with a special attention paid to the relation between symmetries and conserved quantities. Many special cases of motion of the particles in external fields are analysed. Finally, Chap. 3 introduces the Maxwell equations.
The next three chapters provide a discussion of the physical content of the Maxwell-Lorentz electrodynamics in vacuum, with a special emphasis on the the radiation aspect and on the self-interaction problem. Chap. 4 gives an overview of the exact solutions for the electric and magnetic fields. Both static and propagating fields are considered. The main technical tool here is the method of the Green functions. The central topic is an explicit construction of the electromagnetic field configuration that is generated by an arbitrarily moving charged particle. Chap. 5 provides the Lagrangian description of electrodynamics; symmetries and the corresponding conservation laws are discussed in a general framework, and subsequently the special case of Poincaré, conformal, duality, and gauge symmetries are analysed in the separate sections. The summit -the self-interaction problem -is then attacked in the Chap. 6. The author puts into the center the definition of radiation as proposed by Teitelboim and derives the Lorentz-Dirac equation of motion for a