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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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How to implement running of coupling constants in condensed matter

Good evening. I am currently studying finite range corrections to Bogoliubov theory. Basically I assume that $V(q)=g_0+g_2q^2$, as a low energy expansion. While computing some integrals in this area, ...
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Non-local field theory (of Jaffe type) vs strings

As it is well known expectation values of fields are distributions. One usually works with tempered distributions or even with Jaffe fields (https://doi.org/10.1103/PhysRev.158.1454), all defining ...
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Comparing momentum cutoff and lattice regularization in Quantum Field Theory

Usually, it is heuristic to say that we can understand a QFT with a momentum cutoff $|k|<\Lambda$ by imagining that the system is living on a lattice. I would like to ask: (1) Is there any ...
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Is this a correct non-technical description of mirror symmetry for Calabi-Yau manifolds arising from string theory?

In string theory there are physical reasons why the space we live in must locally be the product of Minkowski space with a Calabi-Yau manifold. The general theory doesn't say which Calabi-Yau manifold....
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Does asymptotic safety violate the holographic principle?

As a local QFT, is asymptotic safety compatible with the holographic principle? I read in a blog here about asymptotic safety that it’s incompatible with the holographic principle https://motls....
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Are There Reasonable Definitions Of The Pole Masses Of Light Quarks?

For the heavy quarks and charged leptons, the "pole mass" of a fundamental particle is its mass (which varies as a function of energy scale in the Standard Model) when the energy scale it is evaluated ...
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Massless tadpoles vanish in Baikov representation?

In dim-reg, massless tadpoles vanish. Is it the case also if we use Baikov representation of the Feynman integral?
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confusion about what Wikipedia says about Renormalization

On the wikipedia page, on renormalization, it says the following: "Renormalization replaces the initially postulated mass and charge with new numbers such that the observed mass and charge matches ...
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Understanding field strength renormalization

When it comes to renormalization in QFT I always considered the renormalization of mass and coupling constant as rather intuitive, whereas I found the field strength renormalization rather counter-...
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Why does the RG group flow's linearization provide an eigenbasis at fixed points?

I'm reading Conformal Field Theory by David Sénéchal, Philippe Di Francesco, and Pierre Mathieu. Let $T$ be the map that generates the renormalization (semi-)group by taking couplings $J$ to $J'$ (...
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External structure in BPHZ/Hopf algebraic renormalization of QED

I'm currently trying to understand and reproduce the Hopf-algebraic renormalization of QED presented by Walter D. Van Suijlekom. I don't understand why he chooses these external structures in (2), (7),...
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Is the Standard Model fully renormalizable? [duplicate]

't Hooft showed that Yang Mills theory with spontaneous gauge symmetry breaking Higgs potential is still renormalizable. Is the Standard Model fully renormalizable? The potential issues to ...
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$Z_1=Z_2$ without Ward-Takahashi identity?

In the renormalization of QED, the way that $Z_1=Z_2$ is treated e.g. in Schwartz is by first giving a simple "heuristic argument" based on gauge invariance (in the beginning of section 19.5) before ...
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Renormalization Group (Mirror Symmetry)

In chapter 14 of Mirror Symmetry, one-loop renormalization of the nonlinear sigma model is performed. In Riemann normal coordinates, the interaction term in the Lagrangian is $$-\frac{1}{6}R_{IKJL}\xi^...
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Wilson-Fisher Fixed Point in 2+1 Dimensions

In the paper by y Nathan Seiberg, T. Senthil, Chong Wang and Edward Witten, A Duality Web in 2+1 Dimensions and Condensed Matter Physics it is claimed on page 1 that the two theories $$|D_{B}\phi|^...
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Renormalization of interaction parameter in QCD

In my book of QCD, when talking about renormalization, the author mentions the difference between QED and QCD: In QED, the interaction paramenter $\alpha$ of renormalization factor $\mu$ and ...
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Why can we ignore infinite constant terms that come from constant terms from the Lagrangian?

This is a follow up or better an edit to my previous question that was marked as a duplicate of this other question. I think I failed to emphasize what I really wanted. The tittle of my question was, ...
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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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Beta function for a scalar field theory coupled to gravity

Is it possible to calculate one-loop beta function for a scalar field theory coupled to gravity. If so, can anybody please provide an argument?
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Subtraction scheme in Renormalization [closed]

What is the difference between subtraction scheme used in DREG and counter terms added to the Lagrangian?
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312 views

Shall we skip explicit regularization in the process of renormalization?

In the process of renormalization, regularization is usually cited as indispensable in taming infinities encountered in quantum field theory. Is explicit regularization really necessary? Let's take ...
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Callan-Symanzik Equation Confusion

Consider the standard $\phi^4$ theory: $\mathcal{L}=\frac{1}{2}(\partial_\mu \phi)^2 - \frac{1}{2} m^2_0 \phi^2 - \frac{\lambda_0}{4!}\phi^4$ We define the renormalized field $\phi = Z^{1/2} \phi_r$ ...
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How to get group U(1) from SU(N)?

I have read that the unitary group is somehow given by the direct product $U(N)=U(1)*SU(N)$ and it follows that for $N$ going to zero we get just $U(1)$. How it can be possible? What does it mean $SU(...
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Why does standard model lose predictivity if it has unstable vacuum?

In String Theory In A Nutshell by Elias Kiritsis, Standard Model is unstable as we increase the energy (hierarchy problem of mass scales) and the theory loses predictivity as one starts moving far ...
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Renormalization of Harmonic Oscillator

In Appendix A, Polchinski does the Euclidean path integral for the Harmonic oscillator. After he Pauli-Villars regularizes the determinant of the kinetic term, he obtains the following expression (A.1....
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Renormalization Condition for Fermions

$\require{cancel}$In Peskin & Schroeder chapter 10 page 332 we have the renormalization condition $$\left. \Sigma (\cancel{p})\right|_{\cancel{p}=m} ~=~ 0. \tag{10.40} $$ How is it possible to ...
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Can one calculate scattering amplitudes and cross-sections in string theory?

Can one calculate scattering amplitudes (even tree level) and find cross-sections? Shouldn't loop amplitudes be easier in string theory than QFT because the UV divergences in string theory should not ...
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Why are dimReg divergences power-like? Or are they?

An implicit assumption when working with dimensional regularisation is that the divergences are always of the form $\varepsilon^{-n}$ for some integer $n$ (e.g. refs.1&2). Is there any way to ...
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What is the difference between thermodynamic free energies and the Landau free energy?

How and why is the Landau free energy any different from thermodynamic free energies? It is written on page 140 of Nigel Goldenfeld's book Lectures on Phase Transitions and The Renormalization Group ...
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Form of Renormalized Fermion Propagator

I am calculating a fermionic loop and the expression I obtained for the loop has the form $\not{p}Σ_1(p^2)+Σ_2(p^2)$. Here, $Σ_1$ and $Σ_2$ both have real and imaginary parts. The propagator then ...
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On the Dirac charge quantisation, bare vs. renormalised$.$

Does the Dirac quantisation condition, $ge\in\mathbb Z$ (and its Schwinger-Zwanziger generalisation) refers to bare charges, or (on-shell) renormalised ones? Both options seem natural to me, at least ...
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What can happen on the “other side” of Berezinskii–Kosterlitz–Thouless (BKT) transition?

There is a generalized concept of Berezinskii–Kosterlitz–Thouless (BKT) transition in any dimension [not just in 2 dimensional classical system or 1+1 dimensional quantum system], such that the ...
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How does the renormalization group justify the renomalization process?

I recently learned "Renormalization" and "RG". My textbook says "RG allows us to make sense of why a renormalized quantum field theory describe Nature." To me, it sounds like "RG justifies the ...
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Setting the residue to unity on QFT

I have a question about residues in QFT. I am calculating a fermionic loop and the expression I obtained for the loop has the form $\not{p}\Sigma_1(p^2)+\Sigma_2(p^2)$. Here, $\Sigma_1$ and $\Sigma_2$ ...
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Higgs self-coupling and vacuum stability

I am new to this topic, so I do not have much knowledge of these. When discussing vacuum instability in QFT, higgs self-coupling becoming negative at high-energy scale when renormalized is said to ...
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What is the physical meaning of the renormalized (e.g. $\overline{\mathrm{MS}}$) mass?

In quantum field theory, a subtraction scheme is a way of splitting a Lagrangian $\mathcal{L}$ into a finite piece and a counterterm piece, $$\mathcal{L} = \mathcal{L}_f + \mathcal{L}_{ct}.$$ For ...
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61 views

Existence of loops in Statistical field theory

Since the quantum mechanical formulation of statistical mechanics in canonical ensemble has the terms equivalent to cluster expansion (which can be conveniently written in terms of diagrams similar to ...
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Why is Wilson's work so relevant in particle physics? I thought that critical phenomena were described by CFTs

If I have understood the subject correctly, Wilson correctly explained the second order phase transitions and was able to compute the critical exponents of several of them using the Renormalization ...
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Suppose I have a QFT defined on globally hyperbolic curved spacetimes. Is it renormalizable if its restriction to flat spacetime is?

As the title suggests. I think it should, as changing flat spacetime to slightly non-flat spacetime should not make our theory invalid, as our world is only approximatively flat, and this should have ...
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Suppose QFT is renormalizable. Would curved spacetime extension be renormalizable as well?

Pretty much what title says. We assume that the standard model is renormalizable (What do we mean when we say 't Hooft proved that Standard Model is renormalizable?), but this is for flat ...
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Can the On-Shell Scheme be used for QCD?

I am reading a textbook on QFT and it mentions that the on-shell scheme cannot be used for QCD. Could someone explain the on-shell renormalization scheme in a bit more detail, plus why QCD cannot be ...
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Renormalization in curved spcetime

It is said that renormalization in curved spacetime is difficult. But technically, renormalization procedures can be translated into a problem adding counterterms into Lagrangian. Can't this ...
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Normal ordering in path integral of QFT

In QFT, we use normal ordering to eliminate infinity from hamiltonian. In path integral formulation of QFT though, since what we integrate over is "classical field configuration", instead of operators,...
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321 views

Continuum limit of a free bosonic theory

Suppose you have a bosonic theory in a lattice \begin{equation} H=\sum_{<i,j>}c_1a^+_ia^-_j+c_2(a^+_ia^+_j+a^-_ia^-_j\big) \end{equation} Where $\{a^{\pm}_i\}$ are bosonic creation and ...
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What is the meaning of doing dimensional analysis in Condensed Matter physics?

In QFT, we do dimensional analysis because the superficial degree of divergence is related to the dimension of the dimension of coupling constant, but in Condensed Matter physics, the aim of ...
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Wilsonian RG approach to Fermi liquid theory

In modern terms, Landau's theory of Fermi liquids is understood as the fixed point of a Wilsonian RG as one scales towards the Fermi surface. Shankar and others use the RG interpretation to explain ...
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Does the angular measure matter in dimensional regularization?

In dimensional regularization, we replace a momentum integral $I= \int d^nk f(|k|)$ with the family of regularized integrals $$\mu^{n-d}\int d^dk f(|k|) = \mu^{\epsilon}\Omega_d \int p^{d-1} f(p)dp.\...
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Is there a simple way to understand why SUGRA is two-loop renormalisable?

Naïve quantum gravity is one-loop renormalisable. There is a very simple way to argue that this is true: one lists all possible counter-terms that may appear at one loop, and shows that they are, up ...
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Why do we care about old-style, counterterm renormalizability?

There are a few different definitions of renormalizability that are standard in quantum field theory textbooks. They're all called the same thing, but I'll make up names to make the distinctions clear....
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Renormalisation of non-linear sigma model in 2D

I am following Peskin and Schroeder chap 13.3 on the NLSM. At page 459, eq (13.95), we have to consider the correlator $\langle\partial_\nu\phi_a(0) \partial_\mu \phi_b(0)\rangle$. Because of the ...