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Let us work with charge renormalization in QED. Consider 2-point photon correlation function $\Pi_2(q^2)$ at one loop level. We normalize the coupling constant at $q^2=0$ (point of normalization). What is the effective coupling constant $e(q^2)$ at $−q^2 ≫ m^2$ at one loop level. Does coupling constant decrease or increase with $q^2$?

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It is policy on this site to show where you're stuck exactly in a homework problem and what you have tried. For some background reading: this calculation is a real classic, you should have no problem looking up the details in any QFT textbook (such as Peskin-Schroeder). – Vibert Feb 6 '13 at 11:07
Thank you for the reference, Vilbert. I will take a look at the book and may post a detailed question later. – Muon Feb 6 '13 at 18:38

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