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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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Superfields and the Inconsistency of regularization by dimensional reduction

Question: How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to components)? Background and some references: Regularization by dimensional reduction (DRed) was…
Simon
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Classical and quantum anomalies

I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or points of view: Anomalies are due to the fact that quantum field theories (and maybe quantum mechanical theories…
Diego Mazón
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What exactly is regularization in QFT?

The question. Does there exist a mathematicaly precise, commonly accepted definition of the term "regularization procedure" in perturbative quantum field theory? If so, what is it? Motivation and background. As pointed out by user drake in his…
joshphysics
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Fourier transform of the Coulomb potential

When trying to find the Fourier transform of the Coulomb potential $$V(\mathbf{r})=-\frac{e^2}{r}$$ one is faced with the problem that the resulting integral is divergent. Usually, it is then argued to introduce a screening factor $e^{-\mu r}$ and…
Emerson
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Why do we expect our theories to be independent of cutoffs?

Final edit: I think I pretty much understand now (touch wood)! But there's one thing I don't get. What's the physical reason for expecting the correlation functions to be independent of the cutoff? I.e. why couldn't we just plump for one "master…
Edward Hughes
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Rigor in quantum field theory

Quantum field theory is a broad subject and has the reputation of using methods which are mathematically desiring. For example working with and subtracting infinities or the use of path integrals, which in general have no mathematical meaning (at…
MBN
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Suggested reading for renormalization (not only in QFT)

What papers/books/reviews can you suggest to learn what Renormalization "really" is? Standard QFT textbooks are usually computation-heavy and provide little physical insight in this regard - after my QFT course, I was left with the impression that…
Marcin Kotowski
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Don't understand the integral over the square of the Dirac delta function

In Griffiths' Intro to QM [1] he gives the eigenfunctions of the Hermitian operator $\hat{x}=x$ as being $$g_{\lambda}\left(x\right)~=~B_{\lambda}\delta\left(x-\lambda\right)$$ (cf. last formula on p. 101). He then says that these eigenfunctions…
Peter4075
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Difference between regularization and renormalization?

In quantum field theory we have the concepts of regularization and renormalization. I'm a little confused about these two. In my understanding regularization is a way to make divergent integrals convergent and in renormalization you add terms to the…
Apogee
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Instantons, anomalies, and 1-loop effects

A symmetry is anomalous when the path-integral measure does not respect it. One way this manifests itself is in the inability to regularize certain diagrams containing fermion loops in a way compatible with the symmetry. Specifically, it seems…
user6013
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What's the relation between Wilson Renormalization Group (RG) in Statistical Mechanics and QFT RG?

What's the relation between Wilson Renormalization Group(RG) in Statistical Mechanics and QFT RG? For easier to compare, I choose scalar $\phi^4$ in both cases. Wilson RG: Given $\phi^4$ model, $$Z=\int\mathcal{D}\phi(x)\exp[-\beta…
maplemaple
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Regularization of the Casimir effect

For starters, let me say that although the Casimir effect is standard textbook stuff, the only QFT textbook I have in reach is Weinberg and he doesn't discuss it. So the only source I currently have on the subject is Wikipedia. Nevertheless I…
Squark
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I'm missing the point of renormalization in QFT

I am a qft noob studying from Quantum Field Theory: An Integrated Approach by Fradkin, and in section 13 it discusses the one loop corrections to the effective potential $$U_1[\Phi] = \sum^\infty_{N=1}\frac{1}{N!}\Phi^N\Gamma^{N}_1(0,...,0)$$ And…
physics_fan_123
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Why Does Renormalized Perturbation Theory Work?

I've read about renormalization of $\phi^4$ theory, ie. $\mathcal{L}=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-m^2\phi^2-\frac{\lambda}{4!}\phi^4\,,$ particularly from Ryder's book. But I am confused about something: Ryder begins by calculating…
JLA
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Regulator-scheme-independence in QFT

Are there general conditions (preservation of symmetries for example) under which after regularization and renormalization in a given renormalizable QFT, results obtained for physical quantities are regulator-scheme-independent?
joshphysics
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