Questions tagged [effective-field-theory]

An effective field theory is a systematic approximation for an underlying quantum field theory or a statistical model that includes the appropriate degrees of freedom of phenomena occurring at a chosen length scale (or energy scale), while ignoring substructure and degrees of freedom at shorter distances (or higher energies), summarizing those in its parameters.

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Difference between average effective action and Wilsonian effective action?

There is a good description about " Difference between 1PI effective action and Wilsonian effective action? " here. Now, what is the difference between average effective action, which we use that in ...
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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 upon a time, 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 ...
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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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Does every regularization/renormalization approach gives running coupling constants?

I'm studying different tools for regularization and renormalization. Until now I vaguely understand 1) the wilson approach to renormalization where one thinks of the theory as essencially effective ...
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Srednicki QFT Chapter 29: Feynman diagrams for calculating the effective action

I am trying to work my way through Srednicki Chapter 29 on Wilson's approach to renormalisation. However I am unsure why the Feynman diagrams Srednicki considers and calculates in this chapter are the ...
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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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Can the Lagrangian of an effective field theory have higher derivative terms?

For example, the effective field theory Lagrangian with cutoff $\Lambda$ for the renormalizable $\varphi^4$ theory is $$\mathcal L_{\mathrm{eff}}(\varphi;\Lambda)=\frac{1}{2}Z(\Lambda)\partial_\mu\...
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What does the cut-off $\Lambda$ stand for in the theory of QED?

The bare electron mass $m_0$, in QED, changes as $$m_0\to m=m_0+\delta m\Big(\frac{\Lambda}{E}\Big)$$ where high momentum modes from $E$ to $\Lambda$ has been integrated out. What scale does the cut-...
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Does QED really break down at the Landau pole?

In QED, the fine structure constant $\alpha$ runs upwards in the UV, with a loop calculation (involving a geometric series of the vacuum polarisation diagram) indicating a divergence in $\alpha$ at $\...
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Is it good approximation to use the Fermi theory in terms of proton and neutron for the given processes?

Suppose the processes $$ p+\gamma \to n + \bar{l} + \nu_{l}, \quad p+\gamma \to p+\bar{\nu}_{l} + \nu_{l}, $$ where $p$ denotes a proton, $\gamma$ - a photon, $l$, $\nu_{l}$ - a lepton and ...
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Wilsonian RG and Effective Field Theory

I'm having trouble reconciling the discussions of the Wilsonian RG that appear in the texts of Peskin and Schroeder and Zee on the one hand, and those of Schwartz, Srednicki, and Weinberg on the other....
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Calculation of vaccuum expectation value in Chiral Perturbation Theory

From one point of view I have to admit from the start that this question might be a trivial calculation problem but the truth is, I'm quite stuck. I am studying chiral perturbation theory with the aim ...
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Polarization of Vector particle in high energy limit

In am following this paper : http://inspirehep.net/record/480865 which mentions that (page 9) for a vector particle in the limit $E\rightarrow \infty$, tranverse polarization vector in of $\mathcal{O}(...
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835 views

Calculation of Wilson Coefficients

In Flavour physics, amplitude of decay processes is generally expressed in terms of effective operators (reference). In the framework of effective field theory amplitude $\propto C_iO_i$, where $O_i$ ...
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Infrared and ultraviolet limits of the bulk scalar mass and CFT operator dimension in the AdS/CFT correspondence

On page 131 of these notes, a precise formulation of the AdS/CFT correspondence is given by the GKPW dictionary $$Z_{\text{grav}}[\phi_{0}^{i};\partial M] = \langle \exp \left( - \frac{1}{\hbar} \...
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The irrelevancy of irrelevant couplings in the Wilsonian RG

I have a few questions related to irrelevant couplings in the Wilsonian approach to the renormalization group (RG). What is so great about RG theory is that one can trade the 'real physics', the one ...
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Meaning of perturbative and non-perturbative renormalizability

What is meant by a theory to be (1) perturbatively renormalizable, (2) perturbatively non-renormalizable, (3) non-perturbatively renormalizable, and non-perturbatively non-renormalizable? In each case,...
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The non-renormalizable $\phi^6-$theory as an effective field theory

Let the non-renormalizable $\phi^6$ theory behaves as a low-energy, effective field theory, and works perfectly well below a finite energy (or momentum) scale $\Lambda$ for a system. In this theory, ...
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1answer
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Marginal and relevant operators that a $\phi^4$ theory should contain as an effective field theory

Consider the Lagrangian of $\phi^4$ theory in 4-dimensions $$\mathcal{L}=\frac{1}{2}(\partial_\mu\phi)^2-\frac{1}{2}m^2\phi^2-\frac{\lambda}{4!}\phi^4\tag{1}$$ For a term in the Lagrangian of the form ...
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Dropping yukawa contributions to beta functions when corresponding fermion is inactive?

Consider the two loop beta function for the strong coupling $g_3$, schematically (see eq.98 in https://arxiv.org/pdf/1307.3536.pdf): $$ \frac{dg^2_3}{d \ln\mu^2} = O(g_3^4) + O(g_3^6) + O(g_3^4\:g_2^2)...
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Effective field theories and UV completion

In QCD, there are quarks at high energies, and pions are composite degrees of freedom that appear at low energy where the quarks are strongly coupled. The pion Lagrangian is non-renormalizable; it ...
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Finding the effective Hamiltonian in a certain subspace

In order to find the effective Hamiltonian in a subspace which is energetically well separated from the rest of the Hilbert space people try to find a unitary transformation which makes the ...
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Properties of the nucleons and the nucleus from the interactions between quarks and gluons

Is it possible to deduce the properties of the nucleus or that of the nucleons from the QCD interactions between the constituent quarks and gluons?
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How to calculate annihilation cross section, given effective operator for Datk Matter?

Suppose I have an effective operator of the form $\frac{1}{\Lambda^{2}}$$\bar{\chi}\chi\bar{q}q$, where $\chi$ is an fermionic DM and 'q' is the quark. Given this operator, How do I calculate the DM ...
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Wilsonian picture of renormalization and $\phi^4-$theory

What is the criterion of renormalizability in the Wilsonian picture? In this picture, why is a theory with $\phi^4$ interactions renormalizable and a theory with $\phi^6$ interaction is non-...
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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 ...
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Effective potential in Lagrangian

I have two question related to the steps in equations 3-7 in this paper: Question 1 They find the effective potential in eq. (5) as the negative of the effective Lagrangian (eq. (3)). I don't see how ...
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93 views

Construction of the effective Lagrangian in chiral pertubation theory

The QCD Lagrangian containing quarks and gluons has an approximate $SU(3)_\text{L} \times SU(3)_\text{R}$ which is spontaneously broken by a non-vanishing quark condensate $\langle \bar{q} q \rangle \...
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QCD chPT chemical potential

I have recently been to a guest lecture about low energy QCD with a finite isospin chemical potential. I have two overall questions about this, since it wasn’t possible to ask questions at the given ...
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Lagrangians in field theory and ignorance

The thing that has always bothered me while taking my QFT course was the seemingly arbitrary nature of Lagrangians. For the Klein Gordon equation we just wrote down the simplest Lorentz invariant ...
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318 views

Einstein-Hilbert action as an effective field theory

I have read the following statement: "The Einstein-Hilbert action can be seen as an effective field theory: setting $g_{\mu\nu}= \eta_{\mu\nu}+h_{\mu\nu}$, one gets a free Lagrangian for the field ...
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329 views

Why renormalizable theories are preferred more than non-renormalizable theories?

EDIT: If all field theories, irrespective of whether it is renormizable or not, are regarded as effective field theories. The question is addressed here but there is still a confusion. I was told that ...
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Could the full theory of quantum gravity just be a nonrenormalizable quantum field theory?

This may be more of a philosophical question than a physics question, but here goes. The standard line is that nonrenormalizable QFT's aren't predictive because you need to specify an infinite number ...
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1answer
978 views

The Wess-Zumino term and internal anomalies

Suppose the fermion theory with the global group $G$ spontaneously broken to $G' \in G$. Below the SSB scale we integrate the fermions out and are leaved with Goldstone bosons $\varphi_{i}$ ...
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Coarse graining in the derivation of Boltzmann equation

I am reading chapter 3 of Kardar's statistical physics of particles. I have a question about the coarse grainig. What is the origin of this coarse graining? Is it from the integration of small ...
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1answer
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Standard Model without Electroweak Unification

From what I have read it seems that the Electroweak Unification $$SU(2)×U(1)$$ was developed because the Weak Interaction by itself is non-renormalizable and combining it with the Electromagnetic ...
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1answer
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How can one derive Schwarzian derivative action as low energy effective field theory invariant under global $SL(2,\mathbb{R})$?

In a recent paper (page 47, below eq (4.173)) they make a passing claim that the Schwarzian derivative action can be derived using effective low energy field theory reasoning. I imagine they mean that ...
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chiral partition function - group integral

I am reading this Thermodynamics of chiral symmetry and i really want to know how to perform a group integral, and why it is proportional to the effective action in this case? I have not been able to ...
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How does the naturalness problem of the Higgs mass changes depending on the cut off scale of the Standard Model (SM)?

In this year's paper (check introduction) James D. Wells brings Susskind's 1979 argument that the SM is valid to a very high energy scale, say the Planck scale, $\Lambda \approx M_{Pl} \approx 10^{18} ...
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Are non-renormalizable theories less predictive than renormalizable theories?

Non-renormalizable field theories contain non-renormlizable operators whose couplings have negative mass dimension (for example, Fermi coupling in the Fermi theory of weak interaction). These ...
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What is wrong with a nonrenormalizable theory?

Non-renormalizable theories, when regarded as an effective field theory below a cut-off $\Lambda$, is perfectly meaningful field theory. This is because non-renormalizable operators can be induced in ...
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Effective field theory with coordinate dependent “axion”

Suppose the theory of fermions interacting with EM field and the axial 4-vector $b_{\mu}$: $$ S = \int d^{4}x \bar{\psi}\gamma^{\mu}(i\partial_{\mu} + eA_{\mu} +\gamma_{5}b_{\mu})\psi $$ We want to ...
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1answer
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What does it mean by a nonrenormalizable operator being induced in a Lagrangian?

I have heard that nonrenormalizable operators (i.e., mass dimension greater than 4) can be "induced" in the Lagrangian (that we started with) via loop effects. However, I do not understand what does ...
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Is the Standard model an effective field theory (EFT)?

I've seen both positive and negative answers to this question, though most part of the community seem to agree it can be said it is an EFT up to the electroweak scale. My question is: What are the ...
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Effective Field theory, Super-renormalizable terms and symmetries

I do not know whether I understand the mystery with super-renormalizable terms. Is it that since we can do perturbation theory without paranoia we expect the coupling to be always small enough. But if ...
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1answer
294 views

Relevant interaction terms based on dimension of coupling constants in quantum field theory

For a $\phi^{3}$ quantum field theory, the interaction term is $\displaystyle{\frac{g}{3!}\phi^{3}}$, where $g$ is the coupling constant. The mass dimension of the coupling constant $g$ is $1$ in 4D, ...
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Effective scalar field in terms of the scale on which it emerges

Suppose there is the (pseudo)scalar field $\hat{\theta}$ with non-zero VEV $\theta$, which effectively emerges at energy scale $\Lambda$ (for example, the mass of some fermion, the scale of SSB and so ...
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Is there any software related with effective field theory?

I'm working on standard model effective field theory(SMEFT), I want to improve my calculation about loop correction from higher dimensional operators. But I don't whether those loop corrections can ...
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A few questions concerning one loop corrections to the action [closed]

When we perform a Legendre transform on the connected generate functional $W[J]$ we get the quantum action (or 1PI action) $$ \Gamma[\phi] = W[J(\phi)] - \int\mathrm{d}^4x\,\phi J,\quad\phi(J)=\frac{\...
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Deriving the field equations for a dark energy / modified gravity effective field theory

Question I'm trying to derive the modified gravity EFT field equations and, from their 00 component, this Friedmann equation: \begin{equation} H^{2}+H\frac{\dot{\Omega}}{\Omega}=\frac{\kappa \rho_{m}+...