Is it possible to take a QFT class knowing only basic quantum mechanics? 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)?
 A: 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).
