An elementary resource that goes through basic steps for a computer scientist (non expert in QFT) would be a great. A simpler particle than electron is also ok, but I'd love to understand how you mess with that equation.
Looking at a recent page of that course, the recomended books are
* F. Halzen, A. Martin, “Quarks and Leptons: An introductory course in modern particle physics” (Wiley 1984)
* D. Griffiths, “Introduction to elementary particles” (Wiley 1987)
(and a few more)
The calculation for g=2 is quite easy (for an advanced Physics student). I remember the general idea, but not the details. I think I can reconstruct the details if necessary. It may be explainable in a blog post skipping some details.
The first correction g=2+1/137.036 is also humanly compresible, and can also be explained with some graphics. It would be very hard for me, but if I have a week to seach and rehearsal it is possible.
As the sibling comment says, the following corrections g=2+1/137.036+g=2+?/137.036^2 get harder and harder. And there are too many technical details and problems. I can only see the graphics and get a shallow understanding, but how they are transformed to integral and how to calculate all of them efficiently is too much for my knowledge.
[1] I never finished my Major in Physics, but I finished the one in Math.
It is telling that for a recent course the recommended books are over 35 years old. Consistent with the OP proposition.
* F. Halzen, A. Martin, “Quarks and Leptons: An introductory course in modern particle physics” (Wiley 1984)
* D. Griffiths, “Introduction to elementary particles” (Wiley 1987)
* J.J. Sakurai, “Advanced quantum mechanics” (Addison Wesley 1967).
* P.E. Hodgson, et al., “Introductory nuclear physics” (Oxford 1997).
* H. Frauenfelder, E.M. Henley, “Sub-atomic Physics” (Prentice Hall 1992)
IIRC the Sakurai book is more about generic quantum mechanics, but he has two books, I'm not sure if this has more about particle physics. The other two are more modern, but I don't remember them. I also tried to keep the list short, because usually the main book of the course cover most of the topics.
Anyway, it's a mandatory undergraduate course for everyone that want to be a Physics. If you want to learn cutting edge particle physics, you should take one or two optative course about the topic, then make a one year undergraduate thesis, then take a 5 years PhD, and then perhaps 2 years of a postdocs. So the cutting edge is like 8 years away.
The SM Lagrangian is not computable, so a big part of theoretical physics is about finding tricks to actually compute it.
Incidentally this is why there is disagreement on the muon g-2 discrepancy, at least two theory groups have calculated different values using different approximations.
Also, computing even just one part of this value is basically on the level of a theoretical particle physics dissertation. Don't expect to be able to do this without several years of research experience in this specific field.
https://en.wikipedia.org/wiki/Dirac_equation
The "g" is the Lande g factor:
https://en.wikipedia.org/wiki/Land%C3%A9_g-factor
(As I recall nonrelativistic QM gives g=1.)
PS Not a physicist, but learned some of this at some point. Only ever learned about electrons, though; don't know how any of this translates to other particles.
Caveat-- I work in astronomy but have a PhD in physics and have taken graduate QFT.