In elementary treatments of Wilsonian approach to renormalization group (for example in Peskin & Schroeder, Srednicki, Schwartz, etc.), everybody after chapters of seemless use of dimensional regularization for perturbative renormalization suddenly starts using oldschool hard cutoff which violates Ward identities in QED amongst other things. Is dimensional regularization technicall/conceptually hard or just impossible to use with Wilsonian renormalization approach? Is it avoided because to simplify discussions because the main idea remains the same?
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1$\begingroup$ How would you use dimensional regularization in the Wilsonian context, when the very definition of a Wilsonian theory is that it has an energy scale $\Lambda$ (which is the cutoff in the cutoff renormalization)? Where's the $\Lambda$ coming from in the dimensional approach? See also physics.stackexchange.com/q/394752/50583 and its linked questions for more on the relation between dimensional regularisation and the Wilsonian viewpoint. $\endgroup$– ACuriousMind ♦Commented Aug 22 at 17:07
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