Asymptotic Freedom and the Background Field Method

I presented a group talk for my QFT II class on Peskin and Schroeder section 16.6, explaining the background field method and using it to derive the QCD beta function. I found the section in P&S to be utterly incomprehensible–they don’t really give you any clues to what they’re doing or how anything is defined or what is actually going on. Hopefully the attached notes go some way towards a decent explanation of the background field method. I found Schwartz’s QFT textbook to be much better on this point if you want to read more.