@AbdelmalekAbdesselam Thank you, based on your comment and your linked post it seems I should start studying CQFT immediately and not just focus on the physics. Are there any beginner friendly resources you recommend that introduces some of the basics such as Wightman/Schwinger functions, the various axioms, their uses ...etc?

I have always been a bit intimidated by statistical physics due to my lack of background in the subject, but your post has inspired me to give it a try. I have also been interested in learning about how lattice regularization is carried out but could not find an introduction for a novice such as myself, so those last two links are great! Thanks again!

Thank you for this wonderful and elaborate answer! Since I originally made this post I went through parts of Griffiths' E&M book (skipping anything that was purely computational) and I have a better understanding of field theory now, though at an elementary level. I have also skipped around more of Peskin & Schroeder, but as you mentioned I have found this difficult as someone with only a math background. When you speak of avoiding particle physics, do you mean avoiding P&S-like books altogether?

@TimothyChow Thank you for your suggestion. I actually have a copy of that book and used it as a supplement when going through Folland's book.