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Questions tagged [regularization]

In QFT, regularization is a method of addressing divergent expressions by introducing an arbitrary regulator, such as a minimal distance ϵ in space, or maximal energy Λ. While the physical divergent result is obtained in the limit in which the regulator goes away, ϵ → 0 or Λ → ∞, the regularized result is finite, allowing comparison and combination of results as functions of ϵ, Λ. Use for dimensional regularization as well.

In quantum field theory, regularization is a method of addressing divergent expressions, normally integrals, by introducing an arbitrary regulator, such as a minimal distance ϵ in space, or maximal energy,momentum cutoff Λ. While the physical divergent result is obtained in the limit in which the regulator goes away, ϵ → 0 or Λ → ∞, the regularized result is finite, allowing comparison and combination of results as functions of ϵ, Λ,..., and systematic accounting of the combinations that are independent of, or simply dependent on these. Use for dimensional regularization as well.

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Cutoff regularization: Why not cutoff exactly at the momentum reached in an experiment?

So far I have only actually calculated dimensional regularization and I just know about the idea of cutoff regularization. From what I understand, as the name suggests, you just ignore momentum as from some high value and integrate the virtual…
Jack
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can we PHYSCALLY (not by mathematics) justify that $ \zeta (-s)= 1+2^{s}+3^{s}+4^{s}+... $

the values $ \zeta (-1)= -1/12 $ and $ \zeta (-3)= 1/120 $ give accurate results for casimir and to evaluate the dimension in bosonic string theory so is there a physcial JUSTIFICATION to justify that in phsyics (not mahthematics) every time we see…
Jose Javier Garcia
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renormalization by differentiation how does it work?

i mean let be the integral $$ \int_{0}^{\infty} \frac{p^{3}}{(p^{2}+m^{2})^{2}} $$ logartihmic divergence but if a apply differentiation with respect to $ m^{2} $ i get $$ \int_{0}^{\infty} \frac{-2p^{3}}{(p^{2}+m^{2})^{3}}=I(m) $$ wich is…
Jose Javier Garcia
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Are these IR and UV divergences equal

let be 2 divergent integrals $$ \int_{0}^{\infty}\frac{p^{3}dp}{(p^{2}+m^{2})^{2}}= A $$ $$ \int_{0}^{\infty}\frac{dp}{p(p+q)^{2}}=B $$ B has a divergent as $ p \to 0 $ however i can use a change of variable $ xu=1 $ so for B we have $$…
Jose Javier Garcia
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is the renormalization unique?

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 $…
Jose Javier Garcia
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