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I'm in grad school and notice there are no prerequisites required for QFT in the physics department. In fact, the system allows me to sign up for the course just fine as a technical elective.

But... my field is chemical engineering and I've only taken basic quantum mechanics. I would really love to learn more about QFT though since it's always been something I've really been interested and lightly study in my free time.

From the perspective of someone who knows the physics required to take this course, is the material required to understand the subject outside the range of what I would have learned for an engineer (+QM)?

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@Nick: borrow a copy of press.princeton.edu/titles/7573.html from your college library and try and read the first few chapters. Zee's book is the most accessible QFT book I've found and it will give you a good idea of the maths required. – John Rennie Jan 1 '13 at 8:30
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Nick, quantum field theory is hard but in some sense, it does directly follow "elementary quantum mechanics" in the pedagogic tree. One assumes that you know the quantum harmonic oscillator. If you don't, you will have to learn it at the appropriate moment during the QFT course. Similarly for the angular momentum matrices and representations, the formalism for scattering etc. But in some sense, advanced non-QFT quantum mechanics isn't needed and QFT offers you an alternative formalism that may be the first one where you learn advanced QM. QFT still is a sort of advanced QM and it is hard. – Luboš Motl Jan 1 '13 at 8:34
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Don't worry if you don't feel like you understand QFT the first time around - nobody does. Or at least not us mere mortals. There is a beautiful internal logic to it once it starts to sink in, but that might take a while. The suggestions to try Zee or Peskin & Schroeder are good ones. Another, older book, to try if you can't find those would be Mandl and Shaw. Also try Srednicki, which has a free pre-publication version online: web.physics.ucsb.edu/~mark/qft.html. If you can follow the first chapter or two of any of those books then you are good to go. – Michael Brown Jan 1 '13 at 10:06
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In addition to what Lumo says, it probably helps to understand some complex analysis and for the notation and the physics some (special) relativity. For example I read David McMohans Demystified books in the order QM, Relativity, QFT, and that worked quite well. – Dilaton Jan 1 '13 at 11:26
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@DavidZaslavsky I would leave the question alone, it seems to get reasonable response that is helpful for people who want to study QFT generally. – Dilaton Jan 1 '13 at 11:31

For most QFT classes, it takes a little more than basic quantum mechanics to keep up, especially if you haven't seen any QFT before. It is not necessarily a conceptually hard subject, but it is a lot of new information to take in at once. If you know about Fock space and second quantization, your life is made ten times easier in a QFT course than if you don't. Furthermore, you should be comfortable with linear algebra and complex integration. Also, knowing Einstein summation notation will make the transition from basic quantum mechanics to QFT.

Honestly, a basic quantum mechanics course on its own does not usually cut it. I personally used Baym, Schwabl, and Cohen-Tannoudji for quantum mechanics, and I think those three books prepared me well for QFT. However, I had also taken SR and GR, in which classes I became familiar with Einstein notation.

If you want to know if you are ready for QFT, pick up Peskin and Schroeder and try reading Chapter 2. If you can at least follow it (not necessarily know all the steps for all the derivations), then you could probably give QFT a shot. If not, then you probably need some extra backing in either math (eg linear algebra, complex analysis) or physics (eg SR, QM, EM).

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