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I need to get into QFT because of my thesis, yet I study nothing near physics so I need your guidance how to best proceed. I've got two questions, any answers appreciated:

1) how much QM should I learn? In my book (zettili) I'm in chapter about harmonic oscillator and the rest of the book seems to be occupied by topics such as angular momentum, perturbation theory and scattering theory. Are there any specific topics I should pay special attention to?

2) from other physics, I understand I need special relativity and EM. How much effort I should dedicate to these? Also, my classical mechanics is a bit basic, I know Hamiltons' equations and how to, say, solve simple harmonic oscilator with it, but nothing more advanced, such as Noethers' theorem.

3) the topic that interest me most is renormalization and gauge groups. Any comments how to best prepare for good understanding of these?

Thanks