is the renormalization unique?

Asked Oct 30 '14 at 20:55

Active Oct 30 '14 at 20:55

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mean let be a theory A in which the divergent integrals appear

$ \int_{0}^{\infty}dx $ and $ \int_{0}^{\infty}xdx $

and let be another physical theory with 3 types of divergences

$ \int_{0}^{\infty}dx $ , $ \int_{0}^{\infty}xdx$ and $ \int_{0}^{\infty}x^{2}dx

my question is if $ renormA ( \int_{0}^{\infty}dx)=renormB (\int_{0}^{\infty}dx)$

so all the divergent integrals are renoramlizaed in an unique way

by the way is it true within zeta regularization that $ \int_{0}^{\infty}dx = \sum_{n=0}^{\infty}1=1/2$ in the spirit of zeta function regularization

asked Oct 30 '14 at 20:55

3

This is a fairly cryptic post... – Alex Nelson Oct 30 '14 at 23:34
i am only asking if when you renormalize a UV divergence the renormalization method does not depend on the theory – Jose Javier Garcia Oct 31 '14 at 09:29
also i was asking if within zeta regularization the identity $ \int_{0}^{\infty}dx = 1+1+1+1+1+1+...= \sum_{n=1}^{\infty}1=1/2 $ – Jose Javier Garcia Oct 31 '14 at 13:19

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