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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Is the Aubry-André-Harper (AAH) model renormalizable?

We know the Aubry-André-Harper (AAH) model can have a local/delocal phase transition at $\Delta/J=2$, but can this phase transition point be obtained by RG procedure? Or can this local/delocal phase ...
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Reasons to leave gravity classical in QFT on curved spacetime

From what I have learnt after studying QFT on curved spacetime is that we replace the Minkowski metric, used in flat spacetime QFT, with the general metric and partial derivatives goes to covariant ...
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Non-supersymmetric CFT in $d=4, 5, 6$

There's no known interacting CFT in $d>6$, see Interacting CFT in $d>6$ Also we know a lot CFT in $d=2$ (minimal models for example) and in $d=3$ (WF fixed points in $4-\epsilon$ approach to ...
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Mass in Wilsonian RG (vs. mass in ordinary RG)

The essence of Wilson RG can be described in tree steps: Initially we have some theory on scale $\Lambda$. Lower cut-off $\Lambda^\prime =\zeta^{-1}\Lambda<\Lambda$ and integrate out d.o.f. with $\...
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Emergent supersymmetry in tricritical Ising model

In TASI Lectures on Emergence of Supersymmetry, Gauge Theory and String in Condensed Matter Systems there is statement, that 2d supersymmetry can can emerge from the dilute Ising model: $$ \beta H = -...
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A problem in IR expansion of the effective field theory

On page 43 of Manohar notes on effective field theories, he argues that since all the integrals in EFT are scale less when expanded in terms of the IR parameter, they all vanish. To me it seems ...
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Interacting CFT in $d>6$

There's expectation, that there aren't interacting CFT in $d>6$. As I understand, main reason for this is big dimension of ordinary scalar field, Dirac field. This lead to absence of relevant ...
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Analytic change of free energy after renormalization

Suppose we have some model in statistical physics with Hamiltonian $H$ and partition function $$Z=\mathrm{Tr}\left(e^{-H}\right) $$ the free energy per site is defined as $$ f =\frac1N\log Z$$ A ...
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How could an Effective Field Theory (EFT) have no UV completion?

In the context of quantum gravity, but also in other places, I have heard the question "does this effective field theory admit an UV completion?". However, I really don't understand this ...
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Subtraction in bare perturbation theory on Peskin's book

On chapter 7 of their book on QFT, Peskin and Schroeder derive the vacuum polarization correction to the photon propagator in bare renormalization theory. On page 247, they state that to leading order ...
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Confusion about notation for block transformation in Ising model

I'm going through Cardy's "Scaling and Renormalization in Statistical Physics", and I've run across a notational confusion. Consider a 2D Ising system with the following Hamiltonian $$\...
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Usage of the cutoff momentum in QFT integral

I am trying to calculate the following divergent integral, I cite directly from the book $$\begin{align} V\left(\phi_{c}\right) &=\frac{1}{2} \mu^{2} \phi_{c}^{2}+\frac{\lambda}{4 !} \phi_{c}^{4}-...
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Worldsheet CFT away from criticality

Can we obtain the worldsheet CFT describing string theory as a fixed point of some renormalization group flow (although I assume it leads breaking of diffeomorphism)? In other words, any irrelevant ...
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Finding the form of T with $T(s_1s_2)=T(s_1)T(s_2)$

I'm studying renormalization group theory from "Quantum and Statistical Field Theory by M. Le Bellac". At page 78 he is linearizing the renormalization group transformation around a fixed ...
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Physical meaning of mass renormalization

In the case of charge renormalization, one can present a neat and nice physical idea that brings a physical ground to it called "Vacuum Polarization". Which can be even extended to non-...
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What is the physical interpretation/justification of field renormalization?

In renormalization, we are forced to set several quantities in the Lagrangian to infinite values in order to account for physical results. In QED, for example, we start with a Lagrangian like this: $$ ...
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Relating scaling and critical exponents in the Ising model

I'm reading the chapter about the renormalization group in Yeoman's book "Statistical mechanics of phase transitions" and I'm puzzled about how the author relates the scaling of the RG with ...
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Disadvantages of dimensional regularization as a regularization method

Is there any disadvantage or symmetry violation caused by choosing such regularization method? Like, Hard cut-off regularization that violates gauge symmetry in QED. Is there such a practical instance,...
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Anomalous dimension of the vertex function

I am dealing with the anomalous dimension appearing in the n-point vertex green functions for a change of scale. I am following Ramond book, pages 188-189, Chapter 4, Section 5. Could someone give me ...
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Relevant operators in Ising model

Why in 3d Ising near critical point there are only two relevant deformations? I am interested in experimental arguments and also in theoretical explanation. For example, in 3D Ising Model and ...
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1answer
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On renormalization of $\phi^4$

I am reading Schwartz's chapter on renormalizing the $\phi^4$ theory and I have two questions. We define the renormalized coupling to be the matrix element of all contributing diagrams at a given ...
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1answer
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Identifying the relevant directions in the Ising model renormalization

I'm reading the chapter about the renormalization group in Yeoman's book "Statistical mechanics of phase transitions" and I'm puzzled about how the author relates the scaling of the RG with ...
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116 views

Callan–Symanzik equation, Renormalization, Bare quantities and Green functions relations

I am studying the renormalization procedure from the Ramond book. I understand the computation but I miss some physical insight. I will present my understanding here and the question that I have in ...
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How to expand the QCD loops in terms of infrared scale for matching with heavy quark effective field theory

According to Manohar:"argument applies almost without change to a practical example,the derivation of the HQET Lagrangian to one-loop." on page 37 of the following paper on effective field ...
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Fixed point Hamiltonian for a finite system

Usually when discussing renormalization in statistical physics, some transformation $R$ of the Hamiltonian is defined, and it is supposed that such a transformation has a fixed point $H^*$ such that $...
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Cut-off Regularization - Renomalization - Definition of counter-terms - in Curved Spacetimes

I'm trying to study renormalization in QFT in curved spacetime. So let's say we have a fixed de Sitter background and we have an interacting theory (e.g. massive $\lambda \phi^4$) and I'm going to ...
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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 ...
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RG fixed points and $T_{\mu\nu}$

It is common to refer to fixed points of the renormalization group as scale invariant theories. This statement can be formulated as $$ \beta(\mu) \Big |_{\mu^*} = 0 \; \; \Longrightarrow \; \; T^{\mu}...
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Non-renormalizable theory and mean field theory

For $\phi^4$ theory, when $d>4$, the theory becomes nonrenormalizable, but when $d>4$, we can use mean field theory to calculate the exact critical exponents. The intuition behind mean field ...
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Optimizing MERA disentanglers to represent a specific state

I've read multiple papers (e.g. https://journals.aps.org/prb/abstract/10.1103/PhysRevB.79.144108) on the multiscale entanglement renormalization ansatz (MERA) where algorithms are given for how to ...
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Running couplings and the uncertainty principle

I stumbled across the Wikipedia article on coupling constants [1] and didn't quite unterstand, what the paragraph on running couplings is trying to express. It relates the virtual particles taking ...
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Confusions on QED renormalization

In many QFT textbooks, we usually see the calculations of vertex function, vacuum polarization and electron self-energy. For example, one calculates the vacuum polarization to correct photon ...
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Does the action remain dimensionless after the renormalization?

After the renormalization procedure, fields will gain an anomalous dimension, $\gamma$, which means that their scaling dimension will be different from what we would guess from the dimensional ...
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Why do theories of nature prefer to be renormalizable and not super-renormalizable?

It seems to me (correct me if I am wrong) that all theories in the Standard Model are exactly renormalizable, as opposed to non-renormalizable or super-renormalizable. In a sense, we could say that ...
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Interpretation of Feynman propagator for massive scalar field in position space

I've always treated propagator in the momentum representation so when it diverges, we are on-shell. But what is the interpretation of light-cone divergences in position space? If it is something we ...
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How is $\Lambda_{\textrm{QCD}}$ relevant in the non-perturbative regime?

The famous $\Lambda_{\textrm{QCD}}$ parameter enters through the one-loop running of the QCD coupling, through a relation similar to the following: $$\alpha_S(Q^2)=\frac{\alpha_S(Q^2_0)}{1+b\ln(Q^2/Q^...
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The non-singular term in the transformation of the free energy per lattice site (Or: Is Cardy wrong about the RG transformation)

In Scaling and renormalization in statistical physics by Cardy on page 44 he asserts that the free energy per lattice site defined by $f(\{K\})\equiv-N^{-1} \ln Z$ transforms as $$f(\{K\})=g(\{K\})+...
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Rescaling of effective hamiltonian coupling constants in the Wilsonain renormalization group

I am confused about an aspect of coupling constant rescaling in the Wilsonian renormalization group procedure. (I'm following Kardar's "Statistical Physics of Fields, Ch5). I think I understand the ...
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Is there a difference between renormalization and renormalization group?

Is there a difference between renormalization and renormalization group? In his book 'Scaling and Renormalization in Statistical Mechanics', John Cardy states the following about the term ...
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Question about Renormalization of Ghosts in QCD in MS scheme

During a calculation of the Renormalization constant of the ghosts in QCD I stumbled over the following question: When I calculate the self-energy of the Faddeev-Popov ghosts in $SU(N)$ non-abelian ...
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Electrical conductivity of complex scalar field

I want to compute the conductivity of a complex scalar field in both the symmetric and symmetry broken phases. To define the current operator one needs to couple the matter field to EM gauge field ...
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Pauli Term contribution to muon' s anomalous magnetic moment

I'm trying to compute the contribution of a non-renormalizable term in the QED lagrangian to the muon's anomalous magnetic moment. The term in question is: $\frac{ie}{\Lambda}\bar{\psi}\sigma^{\mu\nu}\...
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1answer
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Renormalization group in statistical mechanics: (1) rescaling of parameters and (2) calculating the free energy

I have some questions about the momentum space renormalization group procedure as described in the textbook "Statistical Mechanics of Fields" by Kardar (Ch5). The first is about the rescaling of ...
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Vertex correction in QED

I've been working through the chapters in Schwartz on the renormalisation of QED, and I have some confusion to do with the form of the Vertex correction. By my understanding, the correlation function ...
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Numerical renormalization of 2D Ising lattice

I'm trying to make some toy computations on the $2D$ Ising model on a square lattice. I want to apply a renormalization transformation, and try to estimate observables on the renormalized lattice ...
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Doesn't the massless $g\phi^4$ theory bound to have an infrared fixed point?

A free, massless scalar theory, $\mathcal{L}_1=\frac{1}{2}(\partial\phi)^2$, is scale-invariant both classically and quantum mechanically. However, a $g\phi^4$ theory, $\mathcal{L}_2=\frac{1}{2}(\...
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$\phi^3$ theories in 2+1 dimensions

I quite often see papers considering a $\phi^4$ theory in three spacetime dimensions, but rarely do I see papers with $\phi^3$ terms. I understand that these kinds of interactions terms can have ...
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References on infraparticles in QED

I recently became interested in a notion of infraparticles as "true" scattering states in, for example, QED. It is well known that S-matrix elements in QED suffer from infrared divergences due to ...
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Computation of beta function for $N$ scalar fields and introduction of deformations

Consider the Euclidean field theory with $N$ real scalar fields $\phi_{i}$ with Lagrangian density: \begin{equation} L=\frac{1}{2}\partial_{\mu}\phi_{i}\partial^{\mu}\phi_{i}+\frac{1}{2}m^{2}\phi_{...
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A bit of confusion with central idea of “running” coupling constants

An effective quantum field theory of a single scalar field $\phi$ is described by an action, $S(\phi,\{g_n\})$ where $\{g_n\}$ denote the coupling constants of the theory. The corresponding path-...

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