The study of classical electromagnetic fields is an adventure. The theory is complete mathematically and we are able to present it as an example of classical Newtonian experimental and mathematical philosophy. There is a set of foundational experiments, on which most of the theory is constructed. And then there is the bold theoretical proposal of a field-field interaction from James Clerk Maxwell. This textbook presents the theory of classical fields as a mathematical structure based solidly on laboratory experiments.
Here the student is introduced to the beauty of classical field theory as a gem of theoretical physics. To keep the discussion fluid, the history is placed in a beginning chapter and some of the mathematical proofs in the appendices.
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Chapters on Green's Functions and Laplace's Equation and a discussion of Faraday's Experiment further deepen the understanding. The chapter on Einstein's relativity is an integral necessity to the text. Finally, chapters on particle motion and waves in a dispersive medium complete the picture. High quality diagrams and detailed end-of-chapter questions enhance the learning experience. It is recommended to students studying classical electrodynamics. A physicist who is a specialist in field theory will enjoy the discussions on subtle points of Maxwell-Lorentz electrodynamics.
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The book will certainly attract the interest of historians of physics. Yaremko, Mathematical Reviews, January, Have seen the Cornell 5-part series about 2.
Let me disagree about index-free notation being simpler than tensor calculus. In the end you risk being swamped by definitions instead of indices, which does not seem like such a great advantage to me. Moreover, finding the right definitions usually involves index manipulation. The reason why the exterior derivative is interesting is that it is a group homomorphism, which intertwines between modules of the group of coordinate transformations i.
If you are interested in manifolds with some extra structure, e. You could perhaps look up these homomorphisms in the literature, but at least the classification of binary and higher homomorphisms is rather recent and not readily available in textbooks. Moreover, I once worked out the exterior derivatives in a case that was not yet published. Some fifteen years ago I was briefly interested in the exceptional Lie superalgebras E 3,6 and E 3,8 , because there is a correspondance between these superalgebras and SU 3 xSU 2 xU 1.
Kac and Rudakov had described the homomorphisms for E 3,6 but had not yet published the result for E 3,8 when I worked it out. The point is that this was done using techniques from tensor calculus and I proud myself of being good at index gymnastics. Often you need to pick a well-chosen set of coordinates and calculate using those.
My point is that it is worthwhile to understand the geometrical, coordinate independent, significance of the objects one is calculating with. A good example is cases in GR where you find solutions with singularities, need to realize these are not physical singularities, but coordinate singularities. David Mermin? I wrote Leonard Susskind some years ago to thank him for these lectures. Well, I learned special relativity out of Spacetime Physics, thereby no doubt dating myself. Perhaps even worse than one might think, since when I first read it Styx was a big band.
Learned GR the classical way, from Rindler.
Peter Woit, I did not talk about choosing coordinates for a specific problem, but rather about expressing the same equations with or without indices. In contrast, tensor calculus can be applied also in unchartered territory. The geometrical meaning of E 3 8 -invariant supergeometry might not be clear, but it was still possible to figure out the analogues of the exterior derivative using index notation. Concerning the index free notation. There exists a combination of both methods, called the abstract index notation see e.
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I think, at least for physicists the abstract index notation has certain advantages, in particular if you have to do some calculations. I had the opposite experience of some. I learned the index notation first, from a physicist, as an undergrad, and I had no idea what in heck he was talking about. None of us did. It starts by giving an insightful but somehow informal explanation of differential and Reimanian geometry and then uses it for introducing EM and GR from a purely geometrical and topological point of view.
It is a really beautiful book. It is a mistake to confuse the use of indices with the use of coordinates. They are two different things. I also found Michors book on Natural Operations which is freely available an eye-opener on categorical methods to help organise the material.
It took me some time to learn, for example, that bundle and sheaf methods were, roughly speaking, dual to each other. And of course calculus itself was once only for the cognoscenti whereas every schoolboy knows about it. Milkshake, Definitely not. Keep in mind that the lectures in that course are mostly the usual material and just about every math department has a similar course with likely a more industrious and more talented lecturer….
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- Springer, Graduate Texts in Physics (GTP).
There are a lot of good textbooks on the subject at this level. As to so-called Abstract Index Notation. And then there is the bold theoretical proposal of a field-field interaction from James Clerk Maxwell. This textbook presents the theory of classical fields as a mathematical structure based solidly on laboratory experiments. The student is introduced to the beauty of classical field theory as a gem of theoretical physics. To keep the discussion fluid, the history is placed in a beginning chapter and some of the mathematical proofs in the appendices. Chapters on Green's Functions and Laplace's Equation and a discussion of Faraday's Experiment further deepen the knowledge.
The following chapter on Einstein's relativity is an integral necessity to the text.
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Finally, chapters on particle motion and waves in a dispersive medium complete the picture.
Related The Classical Theory of Fields: Electromagnetism (Graduate Texts in Physics)
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