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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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Why is $T\overline{T}$ deformation so exciting?

I keep an ear to high energy physics discussions, and one of the things I've heard a lot about recently in these channels is the TTbar deformation (stylized $T\overline{T}$)$^1$. Wikipedia is lacking ...
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Question related to electric dipole moment via QFT

My question is related to the following post: Extracting Electric Dipole Moment from Matrix Element via Form Factor There, it is said that the electric dipole moment (EDM) is giving by a term that ...
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What's the running coupling of gravity?

Pictures like the one below are often used to talk about grand unification. I've never heard any physics textbook really talk about the running of the gravitational coupling constant $G$, but some ...
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Why can't we interpret the W, Z bosons as massive vector bosons not arising from a gauge theory? [duplicate]

The standard story goes as follows: gauge bosons cannot have a mass term because it would break gauge invariance in the lagrangian. This is clear, but why can't we just have massive vector bosons ...
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Asymptotic freedom both in IR and UV

I am wondering if there are any (insightful) examples for models which exhibit asymptotic freedom both in the UV and the IR. I know it sounds odd, but if anyone has come across something like that, ...
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Virtual electron contribution to electron charge

Renormalization, or "a dippy way to to sweep all this stuff under the rug", makes QED the most accurate science ever. I came across a value that explained the difference between the predicted electron ...
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QED infrared divergences

How do infrared divergences arise in QED? What is an example case of such a divergence and how do we usually deal with such divergences? Are they absorbed like ultraviolet divergences?
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If the running coupling constant $\alpha(\mu)$ of QED becomes of order one at high $\mu$, why not changing $\mu$?

In the (modified) MS renormalization scheme, after dimensional regularization, we introduce some parameter $\mu$ with power of mass to keep the dimensionality of integrals under control. The ...
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Wilsonion Renormalization Group in Asymptotically Free Theories

Consider some correlation function computed at some renormalization scale $\mu_0$ in an asymptotically free theory $$ \langle M(z; \mu_o) \rangle. $$ From what I understand of renormalization-group ...
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238 views

“Running with momentum $p$” v.s. “running with renormalization scale $\mu$”

The renormalized charge/coupling in QFT is usually phrased as renormalization scale $\mu$ dependent $\alpha(\mu)$ in the renormalization group setting. But can we take the more elucidating angle of "...
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Anomalous Ward Identities and anomalous dimensions

Let us consider an action $S[\phi,\partial\phi]$ which is classically invariant under a transformation group $G$. The associated Noether current $\mathcal{J}^\mu$ is classically conserved, namely $\...
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$\phi^4$-theory: nested two-loop contribution _8_

Wherever I see calculations of two-loop contributions to the $\phi^4$ propagator (such as Peskin, page 328, on the bottom), only the sunset diagram (aka the Saturn diagram) is considered, but not, say,...
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QED integral is zero in dimensional regularization [closed]

Why is this integral zero in dimensional regularization? $$ \int\frac{d^Dk}{(2\pi)^D}\frac{1}{(k^2)^n} $$
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Divergence of Feynman diagram

Can we say whether the given Feynman diagram is divergent or not by just looking into the Feynman diagram? How to remove these divergences?
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Modified Minimal Subtraction $\overline{MS}$ Scheme advantage

What is the benefit of the $\overline{MS}$ method? Don't we just add some contributions from heavy particles that shouldn't be included in the Vacuum Polarization amplitude since they're way far ...
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How do the renormalization factors disappear from the computation recipe of the S-matrix in Peskin & Schroeder (p. 229 (7.45) & p.324)?

In the following I limit my considerations to 4-point diagrams. After the introduction of renormalized field operator (in renormalized perturbation theory) $\phi_r= (\sqrt{Z})^{-1} \phi$ in eq. (...
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Higgs mechanism and phase transition

Generally speaking, phase transitions divide into two types: First order and second order. To me, Higgs field's SSB sounds like a second-order one though I don't know the dependency of Higgs field's ...
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Cutoff-Scheme Renormalization and Order of Integration in QFT

The following is the result of Fubini's Theorem, describing when you can replace a double integral with an iterated integral safely: For a set $X \times Y \subset \mathbb{R}^2$, if $\iint |f(x,y)| d(...
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Divergent self-energy of point charges in Classical Electrodynamics

Assuming the electron to be a classical point particle, if one calculates the self-energy one finds $$U=-\frac{e^2}{8\pi\epsilon_0r}$$ which diverges as $r\rightarrow 0$. Therefore, the measured mass ...
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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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Correlation functions under rescaling

I was reading this lecture note on Wilson's renormalization group and have hit a snag. I can't obtain equation 5.22. I tried to do the following: \begin{equation} \Gamma^{(n)}_{s\Lambda}(sx_1,…,sx_n;...
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639 views

Hamiltonian of Klein-Gordon Field

The Hamiltonian of the Klein-Gordon Field may be written $$H=\int\frac{d^{3}p}{(2\pi)^{3}}\frac{1}{2\omega_{\mathbf{p}}}\omega_{\mathbf{p}}\left(a^{\dagger}(p)a(p)+\frac{1}{2}(2\pi)^{3}2\omega_{\...
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Doubt about the derivation of the Callan Symanzik equation

I was reading about the Callan Symanzik equation from Peskin and Schroeder. On page 411, they assume that since $G^{(n)}$, the connected Green's function is renormalized, the $\beta$ and $\gamma$ ...
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Renormalization group and counterterms [duplicate]

While regularizing Feynman diagrams, we first isolate its divergent parts and then add counter terms to the Lagrangian in order to subtract out the divergent parts and render the amplitudes finite. So,...
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Power counting and divergences

Often, in many books such as Peskin and Schroeder, a Feynman diagram or the effective potential is expanded as a function of the external momenta or the classical fields respectively. Consider the ...
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Superficial degree of divergence on Weinberg

Reading volume 1 of Weinberg's QFT book, chapter 12, page 505 he says that if you consider a diagram with degree of divergence $D\geq{}0$, its contribution can written as a polynomial of order $D$ in ...
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Why do not renormalization group equations explicitly depend on cutoff?

Suppose $g$ is the parameter set and $\Lambda\equiv\Lambda_0e^{-t}$ the momentum cutoff, then usually one finds the renormalization group equations to take the form $$\frac{dg(t)}{dt}=\beta(g).$$ My ...
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How do you reconcile quark masses with notion of confinement?

In trying to understand exactly what confinement means, I have been reading 't Hooft s original paper on 2D QCD at large $N$. In the paper he shows that the quark propagator pole is moved to infinity, ...
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Inverted propagator in Peskin [duplicate]

Given the Lagrangian (10.18) shouldn't the third diagram in figure 10.3 be the inverse of what has been written?
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Counterterms cancelling divergences

Consider the $\phi^4$ theory. The two divergent Feynman diagrams, namely the two point function and the 4 point function have been isolated and by putting a cut off on their momentum integrations, ...
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Why is gauge invariance so important?

Quantizing the electromagnetic field (without ghosts or gauge fixing terms) using path integrals is not possible because the propagator is not well defined. Textbooks such as P&S or Ashok Das say ...
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What is meant exactly by “renormalization” in condensed matter physics, specifically in density matrix renormalization group (DMRG)?

I first encountered the concept of renormalization in the context of statistical physics. Here, the renormalization "group" is a set of transformations of the system such that the Hamiltonian $H(J,\...
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Is this the picture of a renormalization group flow?

Please look at the cover of this book written by Le Bellac. the book I guess that the picture is about a renormalization group flow (the arrows on the lines). i found a similar picture here here . ...
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Does $ℏ$ play a role in the 1PI effective action?

In most cases, people discuss the effective action or the effective potential in the convention $\hbar=1$. Occasionally, we see the expression at the 1-loop order as $$\Gamma[\phi]=S[\phi]+\frac{i\...
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What is the idea behind coarse-graining?

I don't think I fully understand the idea behind coarse-graining. I will elaborate. I was reading some lecture notes on statistical field theory and the text begins with some previous analyses on the $...
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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 $\widetilde{\phi}$, ...
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Finding the co-efficient of deuteron wave function [closed]

This is the deuteron potential well. The wave functions are given by $$u_{I}(r)=Asin( k_{1}r) $$ $$u_{II}(r)=C e^{- k_{2} r } $$ We have to find the coefficients A an C using continuity and ...
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Why do the Euler-Mascheroni constant $\gamma$ and $\ln 4\pi$ not show up in observables (renormalisation of electric charge)?

The one-loop contribution of the vacuum polarisation of the photon after using dimreg is given by $$\Pi_2^{\mu\nu}= e^2 J(q) \left(\eta^{\mu\nu} - \frac{q^\mu q^\nu}{q^2}\right),$$ with the metric ...
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How does gauge invariance protect the SM gauge boson masses in SUSY from divergent radiative corrections?

The W and Z gauge bosons receive radiative corrections in loop from the heavy SUSY scalars. There is an argument using gauge invariance which explains how the masses remains protected. I am not able ...
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A superficially divergent diagram in $\phi^4$ interaction, rarely appeared in the literature

I'm studying superficial degree of divergence of Feynman diagram and I am confused about some concept. In particular, its scope is on scalar $\phi^4$ interaction in $3+1$ dimension. Some literature ...
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How can the ground state charge be renormalized?

When we calculate the total charge and energy of a quantum field by using Noether's theorem, we find that they are infinitely large, even if we consider a finite spacetime volume_ $$H = \int_V \...
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QFT in in the asymptotic region

Let $\phi(x)$ be a scalar field operator. It often postulate in text books that in the asymptotic region we have $$\lim_{x_0\to-\infty} \phi(x)=\sqrt Z \phi_{in}(x)$$ where $Z$ is a constant. The ...
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Using the Born rule to measure UV divergence?

A typical use of cutoffs is to prevent singularities from appearing during calculation. If some quantities are computed as integrals over energy or another physical quantity, these cutoffs ...
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Multi-dimensional renormalization group flow?

Suppose you have $\lambda \phi^3$ theory, and that you renormalize the 2 and 3 point one-particle irreducible graphs, $\Pi_R(p^2)$ and $\Gamma_R(p_1,p_2,p_3)$, by Taylor expanding about $p=\mu_0$ for ...
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Do vacuum bubbles exist in theories with normal ordered Hamiltonian? [duplicate]

When we calculate the Hamiltonian in the free theory, we notice that it contains an infinitely large term \begin{align} H &= \int_V \mathrm{d }k^3 \frac{\omega_k}{(2\pi)^3 } a^\dagger(\vec ...
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How do self-loop diagrams end up contributing nothing to observables?

The probability amplitude for single particle to enter our system with momentum $k$ and leaving with momentum $q$ can be calculated as \begin{align} A(k\to q ) = \langle q| T e^{i \int_{-\infty}^\...
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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 can we tell a theory is confining?

Physically, I understand what it means for a theory to be confining. The elementary particles are not observable, but only composite particles are. The classic example is QCD, where quarks are ...
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Is there some truth to the often told story that the running of couplings is the result of screening through virtual particles?

It's a well established fact that coupling parameters changes with the energy scale at which we probe a given process: A popular way to explain this phenomenon goes as follows. Particles are ...
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Derivation of the Renormalization Group from Renormalized Coupling?

At page 303 in the book Quantum Field Theory for the Gifted Amateur by Blundell and Lancaster, they argue that the renormalization group equation for the coupling $\lambda$ in $\phi^4$ theory can be ...