Questions tagged [renormalization]

This tag is for questions which relates with the renormalization, an ensemble of techniques which serves to treat the infinities which appear in quantum field theory or statistical mechanics. Renormalization procedures are based on the requirement that certain physical quantities (such as the mass and charge of an electron) equal observed (experimental) values.

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115
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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: ...
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Does the $\frac{4}{3}$ problem of classical electromagnetism remain in quantum mechanics?

In Volume II Chapter $28$ of the Feymann Lectures on Physics, Feynman discusses the infamous $\frac43$ problem of classical electromagnetism. Suppose you have a charged particle of radius $a$ and ...
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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 ...
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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....
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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 ...
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$\operatorname{O}(N)$ sigma model at large $N$

I would like to better understand the main principles of large-$N$ expansion in quantum field theory. To this end I decided to consider simple toy-model with lagrangian (from Wikipedia) $ \mathcal{L} ...
36
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Examples of important known universality classes besides Ising

I am working with RG and have a pretty good idea of how it works. However I have noticed that even though the idea of universality class is very general and makes it possible to classify critical ...
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3answers
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How can dimensional regularization “analytically continue” from a discrete set?

The procedure of dimensional regularization for UV-divergent integrals is generally described as first evaluating the integral in dimensions low enough for it to converge, then "analytically ...
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Renormalization Group for non-equilibrium

For equilibrium/ground state systems, a (Wilson) renormalization group transformation produces a series of systems (flow of Hamiltonians/couplings $H_{\Lambda}$ where $\Lambda$ is the cut-off) such ...
33
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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 ...
32
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Continuum theory from lattice theory

I am looking for references on how to obtain continuum theories from lattice theories. There are basically a few questions that I am interested in, but any references are welcome. For example, you can ...
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Dirac once said that renormalization is just a stop gap procedure, and there had to occur a fundamental change in our ideas. Did something change?

Once, Dirac said the following about renormalization in Quantum Field Theory (look here, for example): Renormalization is just a stop-gap procedure. There must be some fundamental change in our ...
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Why is gravity so hard to unify with the other 3 fundamental forces?

Electricity and magnetism was unified in the 19th century, and unification of electromagnetism with the weak force followed suit, bringing into play the electroweak force. I've been told that ...
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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 ...
29
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Why should the Standard Model be renormalizable?

Effective theories like Little Higgs models or Nambu-Jona-Lasinio model are non-renormalizable and there is no problem with it, since an effective theory does not need to be renormalizable. These ...
29
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1answer
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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 ...
29
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What is the difference between scale invariance and self-similarity?

I always thought that these two terms are some kind of synonyms, meaning that if you have a self-similar or scale invariant system, you can zoom in or out as you like and you will always see the same ...
28
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Difference between 1PI effective action and Wilsonian effective action?

What is the simplest way to describe the difference between these two concepts, that often go by the same name?
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A pedestrian explanation of Renormalization Groups - from QED to classical field theories

shortly after the invention of quantum electrodynamics, one discovered that the theory had some very bad properties. It took twenty years to discover that certain infinities could be overcome by a ...
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Do “typical” QFT's lack a lagrangian description?

Sometimes as a result of learning new things you realize that you are incredibly confused about something you thought you understood very well, and that perhaps your intuition needs to be revised. ...
26
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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 ...
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Triviality of interacting QFT

In this Wikipedia article there are interesting statements: A quantum field theory is said to be trivial when the renormalized coupling, computed through its beta function, goes to zero when the ...
25
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The divergence in QCD Series— How many are they, and what do they mean?

I am referring to this question, and especially this answer. In addition, QCD has - like all field theories - only an asymptotic perturbation series, which means that the series itself will also ...
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What is the Wilsonian definition of renormalizability?

In chapter 23.6, Schwartz's quantum field theory book defines renormalizability as follows, paraphrasing a bit for brevity: Consider a given subset $S$ of the operators and its complement $\bar{S}$....
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What is a good mathematical description of the Non-renormalizability of gravity?

By now everybody knows that gravity is non-renormalizable, what is often lacking is a simplified mathematical description of what that means. Can anybody provide such a description?
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1answer
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Why do irrelevant operators require infinitely many counterterms?

As far as I understand it, in the Wilsonian picture of renormalization, we view a theory as having some fixed cutoff and bare couplings, and integrate out high-momentum modes to understand what ...
24
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1answer
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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=...
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Relation between Wilsonian renormalization and Counterterm Renormalization

Wilsonian renormalization The answer by Heider in this link points out that when we integrate out high momentum Fourier modes, we end up with Wilsonian effective action (not the 1PI action). This is ...
23
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2answers
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In what sense is the renormalization group equation a group?

The renormalization group equation is given by: \begin{equation} \left[\mu \frac{\partial}{\partial \mu} + \beta \frac{\partial}{\partial g} + m \gamma_{m^2} \frac{\partial}{\partial m} - n \gamma_d \...
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If renormalization scale is arbitrary, why do we care about running couplings?

For the bounty please verify the following reasoning [copied from comment below] Ah right, so the idea is that overall observable quantities must be independent of the renormalization scale. But at ...
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What is the relation between renormalization in physics and divergent series in mathematics?

The theory of Divergent Series was developed by Hardy and other mathematicians in the first half of the past century, giving rigorous methods of summation to get unique and consistent results from ...
21
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3answers
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Why is quantum gravity non-renormalizable?

The book The Ideas Of Particle Physics contains a brief treatment of quantum gravity, in which the claim is asserted that if one attempts to construct a model of gravity along the same lines as QED, ...
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QM and Renormalization (layman)

I was reading Michio Kaku's Beyond Einstein. In it, I think, he explains that when physicsts treat a particle as a geometric point they end up with infinity when calculating the strength of the ...
21
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What are the uses of Hopf algebras in physics?

Hopf algebra is nice object full of structure (a bialgebra with an antipode). To get some idea what it looks like, group itself is a Hopf algebra, considered over a field with one element ;) usual ...
21
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1answer
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What does it mean to integrate out fields from a theory?

I've done a fair bit of reading on this subject and I'm still confused about the basic principle of integrating out fields in QFT. When we have a function of 2 fields a and b, f(a,b), and we integrate ...
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1answer
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Understanding the $\phi^4$ phase diagram

I'm having trouble making sense of this phase diagram. The model is a $V(\phi)=g_2 \phi^2+g_4\phi^4$ scalar field theory. Here's what I think I understand: the capital letters represent different ...
19
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1answer
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How do physicists deal with fields at the location of charges?

In the Feynman Lectures Vol 1, Chapter 28 (at the end of section "28–1 Electromagnetism"), it is mentioned: For those purists who know more (the professors who happen to be reading this), we should ...
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Is the Standard Model consistent (UV complete)?

This is a question about the self-consistency of the Standard Model - which I believe is the same as asking whether it is UV complete - in other words, can it be used to predict experimental results ...
19
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1answer
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Renormalization group evolution equations and ill-posed problems

There is a class of observables in QFT (event shapes, parton density functions, light-cone distribution amplitudes) whose the renormalization-group (RG) evolution takes the form of an integro-...
18
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3answers
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Why don't very high order Feynman diagrams contribute significantly?

In a particle physics lecture I had today it was stated that the magnetic moment, $g$, is not quite equal to 2, and the difference is accounted for by QED. Later it was stated that we can see this ...
18
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What is the definition of a “UV-complete” theory?

I would like to know (1) what exactly is a UV-complete theory and (2) what is a confirmatory test of that? Is asymptotic freedom enough to conclude that a theory is UV-complete? Does it become ...
18
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Does renormalization make quantum fields into (slightly) nonlinear functionals of test functions?

Quantum fields are presented as operator-valued distributions, so that the operators in the theory are linear functionals of some test function space. This works well for free fields, giving us a ...
18
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2answers
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Can renormalization group evolution be used to capture emergence?

I am posing this question with condensed matter systems in mind. Is it, in principle, possible to obtain emergence using the renormalization group (RG)? I read in X.-G. Wen's book (Quantum Field ...
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What is the connection between Conformal Field Theory and Renormalization group in QFT?

As I know, the fundamental concept of QFT is Renormalization Group and RG flow. It is defined by making 2 steps: We introduce cutting-off and then integrating over "fast" fields $\widetilde{\phi}$, ...
18
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Values of SM parameters at one certain scale

The general question is: What are the values of Standard Model parameters (in the $\bar{MS}$ renormalization scheme) at some scale e.g. $m_{Z}$? As its parametrization in Yukawa matrices is not unique ...
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Why are we scared of singularities? [closed]

I often hear people say that general relativity predicted its own demise because of the singularities it predicts. If I'm not mistaken, this is also a problem in QFT. I wonder why singularities garner ...
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Renormalization in string theory

I'm taking a course in string theory and have encountered renormalization for the first time (and I suspect it isn't the last). Specifically, while quantizing the bosonic and spinning strings, an ...
17
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What is the difference between pole and running mass?

For example, when we meassure Higgs boson mass to be 125 GeV, do we think about renormalized or pole mass? Should the mass of the Higgs change if it is produced at higher energies?
17
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Can dimensional regularization solve the fine-tuning problem?

I have recently read that the dimensional regularization scheme is "special" because power law divergences are absent. It was argued that power law divergences were unphysical and that there was no ...
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How do we know that nonperturbative canonical quantum gravity is wrong?

In these forums and elsewhere it is routinely agreed that "we do not have a theory of quantum gravity." My question is, how do we know that canonical quantum gravity is "wrong"? I understand that the ...

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