Reference request for Effective field theories

Question

Situation

I've taken a course on QFT, covering canonical quantization (of the scalar, EM and Spinor fields), Feynman diagrams and rules, etc. --- it was your basic one-semester introduction to QFT. I've also had an introduction to the Path integral formulation and was shown how to do basic calculations in it, but I didn't have as much practice in this area as I would wish...

Reference request

I'd like to learn more about Effective field theories (EFT) and of course I've noticed that there is a lot out there covering this topic. Unfortunately, this makes it quite hard to pick a specific resource and follow it.. I've come across a lot of review articles on arxiv (for example [1] and [2]) but there also seem to be some books on the topic (like [3] and [4]). The issue is that I don't know what to pick for my needs. I'd like to read something that gives me a reasonable introduction to the necessary background (i.e. the Path integral formulation seems to be quite important, so it would be nice to have a chapter or so focusing on what properties are relevant, etc.) but even more importantly, I'd like a resource that is as rigorous as possible on the mathematics side.

Answer 1

This article by Polchinski is a classic, and a good introduction to the yoga of EFT for people with some basic QFT background. It is rigorous "enough" in my opinion. What's especially nice about it is how he describes everything by the example of the Fermi liquid, which is just rich enough to be very interesting, but not impossible to understand. He also has a nice annotated bibliography for further reading.