I'm an undergrad and I'll take a graduate-level course on quantum field theory in a month or so, I have studied electromagnetism (one semester course) and a little bit of relativity (on my own), but I'd like to be sure that I have a reasonable understanding of classical field theory. Are there any books/notes/lectures that would help me in such a "short" amount of time? Since I probably won't have that much time to spend on details, the more intuitive, the better.
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Most Quantum Field Theory books I've seen cover Classical Field Theory in the level needed. In this answer, I'll list a few of my favorites when I was learning QFT and some that I found about later.
QFT Books
- Peskin & Schroeder's An Introduction to Quantum Field Theory
This is currently one of the most popular books in QFT. I particularly like to understand the calculations of QFT and how to actually get stuff done, while I have a few different preferences to understading the physical meaning of everything (I'll mention one in a while). P&S covers the basics of Classical Field Theory in the beginning of the book, while it also discusses the need for fields. It will cut straight to the point and most examples will appear as you walk through the book, since fields will be around you pretty much all the time.
Zee loves to chat. His books are often filled with stories, examples, and so on. I particularly enjoy them to understand the physical meaning of things, but he focuses a lot less on computations. His approach will naturally incorporate the path integral formulation of Quantum Field Theory, while P&S chooses to begin with the canonical formalism. In both books, you'll get pretty much what's essential in classical field theory and learn more as you need it (maybe in sort of a sink or swim approach, which I think might be the only way to learn QFT in a single lifetime).
Non-QFT Books
Classical Field Theory can be thought of as Mechanics with infinitely many degrees of freedom, and as a consequence there are books in Mechanics that deal with it. I particularly like Lemos', which is typically mathematically clear (more than most Physics books), but just enough to make things easier to understand instead of diving into a sea of definitions and theorems. Chap. 10 deals with field theory in an excellent way. It is way more detailed than most QFT books (since you won't spend the rest of the semester seeing fields all the time, it has to bring everything together and give more examples) and already gives some familiarity with examples you'll see in QFT (like the Klein–Gordon field and the electromagnetic field), and with examples you've already seem before (like the Schrödinger equation and, well, the electromagnetic field again).
Níck Aguiar Alves
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