Is one semester of quantum sufficient preparation for a QFT course?
What level was your quantum class at and what level is the QFT being taught at?
The quantum class was at the level of Griffiths, and the QFT class is at the level of Peskin & Schroeder.
You will struggle in my opinion (under the assumption that you didn't spend too much time outside of Griffiths studying). I personally feel you need to really dig into QM a couple times before you start really feeling comfortable with it.
As an undergrad I was in your same position. My research adviser really wanted me to take his QFT class because it would have been super useful to me to have seen it for the research I was doing. In the end he decided against it for many reasons: You really should have seen the dirac equation, scattering theory, dealt with spin in QM context extensively, etc.
But only you know if you feel you are ready.
You will need to be very comfortable with Green functions and complex integration. Also, a solid quantum foundation in the harmonic oscillator and dirac notation. It can be done without a solid background in quantum...but to a certain extent your understanding will be superficial...i.e you could probably perform the calculations, but the context will be muddled.
I'm not too fond of peskin personally. I think if you used 'Mandl and Shaw' ,'Schrednecki' and Ryder to compliment Peskin then you might be ok. Also, Griffiths Intro to particle physics has a nice introductory section into QFT somewhere around chptr 11 I think. Introduces the QFT lagrangian for a scalar field and the Euler lagrange eqtns.
There's an interesting blog post by "Flip Tomato" here.
He writes about how to learn QFT as an undergraduate including prerequisites.
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