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is there any mathematical explanation for the UV divergences ??

i have read that in the framework of Epstein-Glser theory :D these UV divergences appear from the product of distributions

anyone does the numbers (divergences) of the form $ \delta ^{(n)}(0) $ have a meaning within the renormalization framework ?? since $ \delta ^{(n)}(0)=i^{n} \int_{-\infty}^{\infty}dx x^{n} $

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I think it's best to start from the works of Wilson and Kadanoff on the renormalization group of effective field theories with an ultraviolet regulator. They find the coefficients can be classified as relevant, marginal and irrelevant. UV divergences are what you get when you run the RG in the other direction.

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