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I found Sean Carroll's "A No Nonsense Introduction to General Relativity" (about page here. pdf here), a 24-page overview of the topic, very helpful for beginning study. It all got me over the hump of learning the meaning of various terms associated with GR, most of which I had heard before without understanding. It also outlined the most important examples.

Is there a similar document for quantum field theory, which presents the main equations, briefly describes the main ideas, and summarizes the most important applications and results so that the reader can feel the lay of the land before studying in depth?

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Gerard 't Hooft's "Quantum Field Theory for Elementary Particles. Is Quantum Field Theory a theory?" (Phys. Rept. 104 nos. 2-4 (1984), 129-142, author's eprint) is a beautifully written review. From the abstract,

What I would like to point out is that renormalizability is just one step in an evolutionary process of quantum field theory. In order to illuminate this point of view I will present a survey of the evolution of quantum field theory into its present form. However we will not follow the historical development, but rather, for my convenience, the lines of logic. As is well known, that is quite something different.

't Hooft also has a longer introduction to the subject:

The conceptual basis of Quantum Field Theory. Gerard 't Hooft. In Philosophy of Physics (J. Butterfield & J. Earman, eds., Elsevier/North-Holland: Amsterdam, 2007). Author's eprint.

This reads more like a textbook geared at readers with fairly solid quantum mechanics and a good understanding of special relativity, and covers a rather wide range of topics, so it is a little more advanced.

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Veltman's book Diagrammatica is awesome when it comes to the basics of field theory and what it all means.

Reading through that one is in my opinion getting it right from the horse's mouth. Not heavy on the calculations but more on how the QFT and it's tools all work together to form a coherent picture of the subject.

It's true that it's a 300 page book, but I think you'll find that it's really easy to read. It's not high powered math and honestly I haven't found anything that got to the heart of the matter as quickly or with less math. QFT is a big subject and GR is more standalone. Reading a chapter in that book will run you about 20 min and it doesn't hurt the brain because it's all stuff an undergrad can easily do. The other reviews of QFT I've seen are very technical and extremely dense. Let me know if you find a better shorter alternative: I'd like to read something that succinct myself!

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There is a great introduction called "This is How Quantum Field Theory Works" which, I think, is exactly what you are looking for.

All essential concepts are introduced and the basic idea how one gets from the fundamental equations to cross sections, i.e. quantities that can be measured in experiments is sketched.

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  • $\begingroup$ @MarkEichenlaub which Lagrangian changes if we change into what reference frame? $\endgroup$ – Tim Jun 20 '15 at 12:43
  • $\begingroup$ The link above seems dead. I don't know if this is the same thing (sounds like it), but at least on my browser, the math is not formatted correctly. $\endgroup$ – NickD Oct 12 '17 at 15:21
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Feynman's book QED: The Strange Theory of Light and Matter is probably your best bet. He spells out what is going on in the equations of quantum electrodynamics in about 120 pages and briefly touches on how these equations generalize in other parts of QFT.

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Yes, it is by a German author who spends most of his time writing books which are pedagogic and student-friendly. He is Jacob.

And he has written a book entitled "No-Nonsense Quantum Field Theory: A Student-Friendly Introduction" You could get it here in Amazon or Gumroad.

He has written the textbook covering all basic and major aspects in a conversational style which is like a final year graduate explaining and advising all the pitfalls and misconceptions he has faced when he was learning to a Sophomore.

PS: The above links are not affiliated links.

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The dead links to This is How Quantum Field Theory Works seem to host some dodgy stuff now. The Internet Archive has a copy at 2016-10-21: https://web.archive.org/web/20161021150828/http://physicsinsider.com/this-is-how-quantum-field-theory-works/

Summary: We talk about the most important concepts of quantum field theory and why they are important. You’ll learn how to compute the probability that certain new particles are created if we smash two particles, for example electrons, together. You’ll understand how particles can be described in a field theory. Let‘s start with some good news: quantum field theory is easy, especially if you already know how quantum mechanics works. Of course, not every computation in quantum field theory is easy, but understanding how the framework works in principle is.

Contents: 1 Essential Concepts 1.1 Why a field theory? 1.2 The Lagrangian Formalism 1.3 The Quantum Formalism 1.4 Noether’s Theorem 1.5 Spin 1.6 Field Equations and their Solutions 1.7 The Canonical Commutation Relation 1.8 Solutions of the Field Equations 1.9 The Hamiltonian 1.10 Creation and Annihilation Operators 1.11 The Scattering Operator 1.12 Time Evolution 1.13 Gauge Theory and Interactions 2 How Quantum Field Theory Works 3 Recommended Books

It provides a short (couple of pages) overview of Quantum Field Theory. Equations look Latexy (at least on the latest Firefox), though there are not too many derivations in this text.

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