Questions tagged [renormalization]

Renormalization is an ensemble of techniques which serves to treat the infinities which appear in quantum field theory or statistical mechanics.

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Intuition for Asymptotic Freedom

In QED, the $\beta$-function has a positive sign. This means that the coupling increases at higher energies, or equivalently, smaller length scales. This picture is made intuitively clear by the ...
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How to do Inverse Mellin Transform of quark-in-quark Anomalous Dimension

The evolution of quark parton distribution functions (pdf) can be described as a resummation of gluon emissions from scale $Q_0^2 \rightarrow Q^2$ via DGLAP equation (in valence sector): $$ \mu^2 \...
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Renormalization and fluid dynamics

Both Quantum Field Theory and fluid dynamics rest upon discarding finer details of the system and/or small-scale degrees of freedom. I understand that both frameworks require such removal ...
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Finding and diagonalizing the mass matrix

I'm trying to find the mass matrix from the actions in $(2.10)$ and $(2.11)$ in this paper. The action is expanded around a classical background field $B^{i}$ and the action for fluctuations is given ...
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Renormalization when there is spontaneous symmetry breaking

Standard quantum field theory textbooks discuss spontaneous symmetry breaking with the following Lagrangian: $$L=\frac{1}{2}\partial_{\mu}\vec{\phi} \cdot \partial^\mu \vec{\phi}+m^2\vec{\phi}\cdot \...
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Higher dimensional operators in Srednicki's EFT

In Mark Srednicki's QFT book in chapter 29, page 187 he talks about the leading contribution of $c_{d,i}$ being given by a 1-loop diagram with 2n external lines representing $|k| < \Lambda$ momenta,...
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Renormalization group and summation of diagrams

Currently I'm studying renormalization group, and I'm having trouble understanding the following statement which I see almost everywhere in books on QFT: renormalization group sums a series of ...
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Is there a general behavior of energy gap under renormalization?

Perform real space renormalization on a discrete lattice model with a finite energy gap. Is it always true that under the flow of coarse-graining, the energy gap will only increase? I think the ...
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Ward identity prohibits mass of photon

On wikipedia one can read the following statement: The photon and gluon do not get a mass through renormalization because gauge symmetry protects them from getting a mass. This is a consequence of ...
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Renormalization of the $O(N)$ vector model - integral

I am following the steps made in the review https://arxiv.org/abs/1512.06784. there, at page 14 the author proceeds to find a specific logarithmic term for $\frac{\partial U_{eff}}{\partial \sigma}$ ...
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Field strength renormalization and the energy-momentum tensor

This question is about the connection between the energy-momentum tensor, dilation transformations, and field renormalization. From a Wilsonian perspective on renormalization we start out with a ...
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How the hierarchy of forces is explained by Supersymmetry?

The hierarchy problem is often stated in two ways: First, the divergent corrections to the Higgs bare mass, second, why is gravity so much weaker than the other three forces. The solution to the ...
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How is there no hierarchy problem without UV cutoff?

I can understand the quadratic divergent corrections to Higgs bare mass which is referred to as the hierarchy problem. But I don't understand how there won't be any hierarchy problem if we do not ...
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$CP^N$ model in Peskin & Schroeder problem 13.3

In Peskin & Schroeder exercise 13.3 question d, it is asked to perform an expansion of the term $$iS =-N.tr\left[\log\left(-D^2-\lambda\right)\right]+\frac{i}{g^2}\int d^2x \lambda $$ where $D_{\...
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Renormalization of minisuperspace models

It often appears in the literature that the full quantum gravity theories are plagued by the quantum field theory problems, specially non-renormalization. And they also state that in the context of ...
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Intuitive explanation of superficial degree of divergence

Consider $\varphi^p$ theory in dimension $D$. For a Feyman diagram $\Gamma$ one can introduce the superficial degree of divergence $deg(\Gamma)$. It is defined as $DL-2I$ where $I$ is the number of ...
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Regularization methods' equivalence and the hierarchy problem

There are several questions related to this one but whose answers just raise the doubt I'm going to describe here. Some facts that are everywhere are (i) The hierarchy problem results from the fact ...
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The importance of dimensions in the effective Lagrangian

I would like to examine the contributions from the new physics in any process in particle physics with the help of the Effective Lagrangian method. In this method, the standard model Lagrangian plus ...
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Do we care about CFTs in particle physics?

This question is related to these others: mostly this one, but also this one and this one. Do we care about CFTs in particle physics? Let me explain. Suppose we don’t know anything about string ...
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Why is the beta function in RG usually defined as a “logarithmic” derivative?

What is the motivation behind defining the beta function as the logarithmic derivative of the coupling constant with respect to scale and not just the regular derivative?
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Perturbing about the Renormalized Field Theory: What justifies perturbing if the counter-terms are large? [duplicate]

I have a very basic question about Renormalization in Quantum Field Theory. Consider the following passage (about $\phi^4$ theory) from Zee's Quantum Field Theory in a Nutshell (from Chapter III.3): ...
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On scheme dependence in QFT renormalization

I searched for the answer to my question quite a while and it seems nobody ever asked similar questions or it is written explicitly in any textbooks. The question is, If physical parameters of any ...
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Renormalization scheme dependence

Is it possible that the QFTs at hand show dependence on the renormalization point at which renormalization conditions are introduced?
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Making the most general lagrangian of triplet scalar fields under $SU(3)$ symmetry

I need to write the most general renormalized lagrangian under those conditions: The symmetry is global $SU(3)_G$ There is 3 triplets of scalar field $\phi(3)_i$ , $i=1,2,3$ There are no fermion ...
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RG of Ising model whose Hamiltonian is represented with Kronecker delta

Let $H$ be hamiltonian, $i$ the index of a spin, and $S_i = \pm 1 $ the $i$-th spin's value. When 1D Ising model's hamiltonian is represented as $$ H = - J \sum _i S_i S_{i + 1}\ \ \ (J > 0), $$ ...
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Are there known expressions for the running of $\alpha_{em}(Q^2)$ and $\sin^2(\theta_{W})$?

I'm doing some integrations in Hadron physics, involving form factors and the like, and these terms show up often. I can get okay results if I use the values these couplings take at $Q^2=0$, but a ...
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What does QCD look like in higher dimensions?

It was pointed out as a comment on my question on atomic physics in higher dimensions that that question implicitly rests on an assumption that QCD, and thus the structure of atomic nuclei, is pretty ...
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A Question about Wave-Function Renormalization Factor in SQCD

Here, I have a question about the one-loop computation of the wave-function renormalization factor in SQCD. According to Seiberg duality, the following electric $\mathrm{SQCD}_{e}$ \begin{gather} ...
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(Coleman's lecture note) scattering in QFT

I am currently reading Coleman's lecture note on QFT.(https://arxiv.org/abs/1110.5013) I have several questions regarding the scattering theory. Let $\phi$ be a real scalar field, and consider the ...
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What's the exact relationship between the scale $Q$ at which parameters are probed and the “fake parameter” $\mu$?

It is well known that couplings change depending on the scale $Q$ at they are measured. This effect is experimentally well documented: From a theoretical point of view, the running $\alpha_S(\mu)$ ...
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Kosterlitz-Thouless transition and renormalisation group theory [closed]

I'm trying to understand the Kosterlitz-Thouless transition in 2d systems. There is a section in Altland and Simons' Condensed Matter Field Theory that discusses the phenomenon, but I don't really ...
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What's the difference be Wilsonian and continuum EFT?

In his review on Effective Field Theory, Georgi emphasizes Within the general framework of the effective field theory idea, there are two rather different approaches, which I will call the Wilson ...
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Regularization is mandatory. What about renormalization?

We need to regularize in order to declare with confidence that infinities drop out from measurable quantities, e.g. in the form of a cutoff scale. In general, the amplitudes in QFT depend on the ...
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How do we end up with the renormalization group equations in the Wilsonian perspective?

We start with a Lagrangian $L$, which is valid up to some scale $\Lambda$ and includes couplings $g,m$. In the Wilsonian perspective, we note that the contributions from fluctuations at scales ...
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Why sharp cutoff RG introduces long range interaction and smooth cutoff doesn't

In momentum shell RG we introduce a sharp momentum cutoff, and integrate out those high momentum modes to get an effective action. I heard that this kind of RG will introduce long range interaction, ...
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Why the randomness in glass/water/air does not destroy coherence of light over fairly macroscopic scales?

When light passes through glass/water/air, photons are absorbed and re-emitted by the chemical bonds, so that the speed of light in medium is reduced. However, in these media, it would appear that the ...
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Why can a renormalizable quantum field theory only include spin 0, 1/2 and 1 fields?

Hitoshi Murayama writes in his 221A Lecture Notes on Spin How do we choose spin when you introduce a field, then? A consistent ( i.e. , renormalizable) quantum field theory can include only spin 0, ...
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Where the derivative corrections come from in Wilson renormalization?

I known that in the Wilson renormalization process fast modes are integrated out in order to define an effective action for the low modes field. Considering phi to the fourth theory it's easy to see ...
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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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Wheeler-deWitt equation as a renormalization group flow

I recently heard a comment that Wheeler-deWitt equation can be interpreted as RG flow equations. However, I haven't been able to find appropriate references for the same. Could someone suggest any ...
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One-loop corrections to vacuum polarization with a specific Lagrangian

I'm having some difficulties regarding this problem in QFT I'm doing to prepare for an exam. For the following problem I consider the theory described by the Lagrangian: $$\mathcal{L}=-\frac{1}{4}F_{\...
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Why don't we add Wilson loops to the SM Lagrangian?

As the title says: why don't we add Wilson loops to common Lagrangians such as the Standard Model? They're gauge invariant and (correct me if I'm wrong, not sure on that) are renormalizable. Suppose ...
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Why/When would one study Renormalization Group flow of a system?

It is not that I am looking for a cheap way out of reading a book about RG flow, but I would like to know few key insights that RG flow study provides, backed with some specific examples. I know a ...
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What are the necessary or sufficient conditions for a renormalization group scheme to be “valid”?

Suppose I have a super operator $G$ which acts on Hamiltonians to produce a new Hamiltonian that is related somehow. For the purposes of this question, suppose that these Hamiltonians are defined on ...
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Tadpole diagrams in 1-loop massive scalar amplitudes?

Consider a massive scalar diagram such as or The loop momentum enters and exits the tadpole vertex, so that in the first diagram the momentum in the propagator connecting the two vertices is zero ...
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Is it possible to define a real space renormalization group scheme for a lattice where the local Hilbert space dimension increases?

I'm currently looking at a way of renormalizing a particular Hamiltonian. One of the questions I'm currently trying to answer is whether, in a renormaliztion group (RG) flow, it is valid to allow the ...
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Peskin and Schroeder Section 7.1 Mass Shift

I'm slowly reading my way through Peskin and Schroeder. Near the end of section 7.1 they compare the mass shift of the electron from QFT to the classical value, both of which are divergent but in ...
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Bare mass versus the mass form spontaneous symmetry breaking

Consider renormalization in $\phi^4$ theory $$\mathscr{L}=(\partial\phi)^2-\frac{1}{2}m^2\phi^2+\frac{\lambda}{4}\phi^4$$ where $m$ and $\lambda$ are respectively the unobservable bare mass and bare ...
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In relativistic QFT, is it ever possible that the bare mass be finite and equal to the physical mass?

In renormalization, one follows the philosophy that the bare mass is unobservable and could be infinite, and the physical mass comes from the pole of the two-point function. Is it possible that in any ...
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Renormalization constants

I would like to understand how to extract renormalization constants of vacuum polarization diagram in pseudoscalar Yukawa theory with interaction $ig\bar{\psi}\gamma^5\psi$. This diagram is ...