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at effective quantum field theory I have started writing an Idea-section and added more reference
In my memory, there were at least two distinct notions of effective field theory, as my colleagues in Wisconsin, like Ted Allen, used to say, “ordinary” and “Wilsonian”.
Hm, okay. I am not sure. I should try to educate myself better about some details.
It is somewhat remarkable how many things about effective QFT are not in the folk lore. For instance the standard statement that computing perturbative quantum gravity effects is impossible due to non-renormalizability is simply wrong. As an effective QFT gravity is as good as any other. In fact even better, as that introduction by Donoghue nicely emphases. He explicitly computes a quantum gravity effect there.
For these questions on what is and what is not possible about quantum gravity, I heard very interesting ideas form Jarah Evslin including that the finite age of universe may be relevant!He was thinking about that a lot and has many alterantive proposals.
Wilsonian vs 1Pi effective actions in particle physics (I am not sure if this is the disctinction we were talking at the time ago):
http://particlephd.wordpress.com/2009/08/17/wilsonian-vs-1pi-actions
I remember at the time when Seiberg-Witten (at the time in N=2 incarnation) stuff appeared we had some series of journal club seminars, and one of the references was emphasising that it was not an ordinary but Wilsonian action. I had to prepare a talk for the latter for the next week, but I was too busy and did not. Then the seminar broke for few weeks and eventually I never gave that seminar.
I have now filled in content spelling out the rigorous formulation of effective quantum field theory in terms of causal perturbation theory, following Fredenhagen-Dütsch et. al.: here.
Incidentally, regarding #2 above (from many years ago): This rigorous formulation allows a simple proof that the standard effective action $S_{eff}$ (in the sense of Feynman perturbation series over connected diagrams) does equal the Wilsonian effective action $S_{eff,\Lambda}$ for $\Lambda \to 0$ (this prop.). This is generally a point of confusion in the traditional non-rigorous formulation (e.g. Physics.SE discussion here).
I should eventually split off some little entries from the new material at effective QFT that deserve being stand-alone, such as UV cutoff, counterterms, Polchinski’s flow equation and maybe Wilsonian RG. Right now all these terms redirect to effective QFT.
I wrote:
I should eventually split off some little entries from the new material at effective QFT that deserve being stand-alone, such as UV cutoff, counterterms, Polchinski’s flow equation and maybe Wilsonian RG. Right now all these terms redirect to effective QFT.
I see now that a stub entry counterterms already existed. So I have now expanded there a little, for the moment with pointer to the material at effective QFT. For completeness I have then also split-off interaction vertex redefinition as a separate entry (which used to redirect to Stückelberg-Petermann renormalization group).
I have spelled out the proof of “Polchinki’s flow equation”: here.
(For entertainment you should compare to the original account in Polchinski 84, (27).)
[edit: so I have split this off as a stand-alone entry: Polchinski’s flow equation]
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added pointer to this relatively new textbook:
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