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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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The way you've phrased the question, Nick, I don't think it's on topic here. We can't tell you whether you can sign up for a particular class. If you were to ask instead "Is it possible to take a QFT class knowing only basic quantum mechanics?" then it might be better. Let me know if you do that and I'll reopen the question, and we'll see what the community thinks about it. –  David Z Jan 1 '13 at 8:13
    
Isn't that somewhat pedantic? That is certainly my intent with the question. –  Nick Jan 1 '13 at 8:15
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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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@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
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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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