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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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Understanding irrelevant operators in Wilsonian RG

I had always understood irrelevant operators as operators whose coefficients got smaller at lower energy scales, but there's a passage from Schwartz's Quantum Field Theory and the Standard Model which ...
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How does the generalized effective action in Wetterich's exact RG scheme relate to observables at different scales?

I am not familiar with Wetterich's exact RG paradigm, and cannot understand the main idea behind it. I understand that if one could have solved the model and obtained the all the n-point functions ...
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Unit of pion-decay constant

In the natural unit system, the pion-decay constant $f_{\pi}$ is $92.4\:\rm MeV$. But I think that a decay constant should have a dimension of $[T]^{-1}$, where $[T]$ is the dimension of time. Then, ...
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Effective field theories from QCD

Is there a way - at least formally - to derive theories like chiral perturbation theory or heavy baryon effective theory from QCD? As an example: is it possible first to introduce the effective ...
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Why does the Lagrangian Density have to be a polynomial of the field?

In a lecture, a professor appeared to have said that the Lagrangian can only contain terms that have powers of $\phi$ and a term with $\partial_\mu \partial^\mu \phi$ . I imagine this would make any ...
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${\cal N} = 1$ SUSY Non-renormalization theorem

In Ref. 1, on Page 53, the ${\cal N} = 1$ SUSY non-renormalization theorem is derived. One first specifies the symmetries of the general ${\cal N} = 1$ SUSY action in the superspace formalism, and ...
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Why is the standard model renormalizable if we believe it is an effective theory? [duplicate]

We believe that the standard model is only an effective field theory of its true UV completion. However, effective theories have dimensionful couplings and are not renormalizable. The standard model ...
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High-energy effective field theory

Usually when one speaks of effective field theories, one is looking to integrate out certain fields which are typically heavy in comparison to the regime of interest. That is one has a theory at a ...
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107 views

How to fuse quantum mechanics and general relativity?

I am very new to this topic but I have started reading Kevin Wray's lecture notes about string theory (PDF) and in the introduction he says: "Sometimes it is said that we don’t understand how to ...
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Computing the Wilsonian Action

Equation 12.5 of Peskin&Schroeder reads $$Z = \int\left[\mathcal{D}{\phi}\right] e ^{-\int d^dx \, \frac{1}{2} (\partial \phi)^2 + \frac{m^2}{2}\phi^2 + \frac{\lambda}{4!}\phi^4} \cdot \...
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Why is vanishing beta function associated with scale-invariance?

Why is vanishing beta function associated with scale-invariance? Coupling constants have change rate of zero at some scale, but how is that related to scale-invariance? Association of vanishing beta ...
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Symmetries of effective field theory of hydrodynamics: a confusing calculation

This is a very specific question about a paper by P. Glorioso and H. Liu that can be found here https://arxiv.org/pdf/1805.09331.pdf. In particular I want to understand how the authors get from the ...
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Is there any threat to the results of our effective field theories from unknown higher energy theories?

We use renormalization arguments (and experiments) to change the couplings of a theory and suppress the higher energy physics (saying things like “whatever the fundamental theory, this will be true of ...
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Can a unified physics theory have a smaller number of couplings than its effective field theory?

Suppose that we have a QFT that has $n$ number of physical coupling constants, or there are $n$ coupling constants required to perturbatively renormalize the given QFT. Suppose this QFT to be an ...
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Recovering nonrelativistic quantum mechanics from quantum field theory

In quantum field theory -- specially when applied to high energy physics -- we see that the requirements of Lorentz invariance, gauge invariance, and renormalizability strongly limit the kinds of ...
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QED vertex correction, proper vertex function and meaning

I might be making great confusion in trying to interpret proper vertex function. I'm studying QED vertex correction. I'm just going to write down the pieces of the puzzle. So I know that the ...
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What's the “effective potential” for photons in $X$-ray diffraction?

The slickest way to introduce $X$-ray diffraction is to invoke scattering theory in quantum mechanics. One treats the incoming photon as just another particle in a scattering problem; by Fermi's ...
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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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What does soft symmetry breaking physically mean?

A symmetry can be explicitly broken by adding terms in the Lagrangian that aren't compatible with the symmetry, and we say the symmetry is softly broken if all these terms have positive mass dimension....
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Invariant terms of Chiral Lagrangian

Stupid question. Consider a global SU(N) theory spontaneously broken. I want to write the EFT of the Goldstone bosons in terms of the field $$ \Pi = e^{i\pi^a T^a} $$ where $T^a$ are the SU(N) ...
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Feynman rule of $\bar{\phi} \phi F_{\mu \nu}F^{\mu \nu}$ and its corresponding 4-photon scattering amplitude

Consider the Lagrangian: $$\mathcal{L}~=~-\frac{1}{2}\bar{\phi} \square \phi - \frac{1}{4}F_{\mu \nu}F^{\mu \nu} + \lambda \bar{\phi} \phi F_{\mu \nu}F^{\mu \nu}$$$\hspace{200px}$ The vertex Feynman ...
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Lorentz invariance hereditity from fundamental to phenomenogical models

I'm taking the courage to ask here a question that could be proven naive- if so, it should be closed and I will delete it. If we assume a QFT with Lorentz invariance, is there a way to show, besides ...
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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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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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Can dimensional regularization be viewed as a soft version of a Wilsonian cutoff?

In the Wilsonian picture of renormalization, a quantum field theory is defined to have degrees of freedom only up to an energy scale $\Lambda$. The results of low-energy experiments shouldn't change ...
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The 3 graviton species

Recently, there is some speculation about the fact that quantum gravity could imply the existence (naturally, even without extra dimensions or any other stuff) of 3 gravitons: a massive spin-2 ghost ...
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Perturbative renormalization and Wilsonian approach

It is not clear to me that the perturbative renormalization and the Wilsonian approach must coincide. Indeed the perturbative renormalization procedure does not seem similar to that of integrating out ...
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Fermionic CW potential unbounded below for large background?

I'm studying the Coleman Weinberg potential in presence of the background Higgs h. It seems to be well known that the CW potential goes like $(-1)^F m^4 \log(m^2)$, where $m^2$ is the background-...
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Diagram versus gradient expansion

Suppose one starts from the Dyson equation $\int dy\left[G^{-1}\left(x_{1},y\right)\cdot G\left(y,x_{2}\right)\right]=\delta\left(x_{1}-x_{2}\right)$ with $G$ some Green's function. One may usually ...
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Einstein's equation in D dimensional space

Under the framework of Large extra dimension. Reference paper Page 9 to 10 Suppose $g_{AB}=\eta_{AB}+\frac{1}{2M_D^{1+\delta/2}}h_{AB}$ When we write the $$h_{AB}(z)=\sum\limits_{n_1=-\infty}^\...
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225 views

How does 11D Supergravity relate to M-Theory?

I know Type IIA/B, Type I, HO, & HE are related through the T and S Dualities. However, how does SUGRA factor in here? What exactly is 11D SUGRA’s significance in M-Theory? Some seem to suggest ...
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What is the meaning of the Wilson coefficients $C_{S,P,T}$ in the electron-nucleon interaction?

I am doing a project on electric dipole moments in supersymmetry. My background is in high energy physics, so I am having trouble fully grasping the nuclear interactions. Part of that includes ...
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pNRQCD at high pT

pNRQCD is an effective field theory for heavy Quarkonium, where the velocities are non-relativistic due to large mass. But is pQCD applicable when the Quarkonium is moving at high velocities? The ...
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Renormalising $\Delta$ baryon mass in chiral effective field theory

I have essentially no experience of quantum field theory, other than a superficial knowledge of some basic ideas - my apologies if I've phrased anything unusually or made any mistakes in my question ...
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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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What diagrams to include in Wilson's Approach?

In the Wilson's approach to renormalization we split the field into two parts; a high momentum part and a low momentum part. We then integrate out the high momentum terms. Consider the case of $\phi^3$...
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Do we “get rid of” irrelevant operators in as we consider low-energy effective theory?

On reading the section 12.1 of Peskin and Schroeder's (P&S) QFT on "Wilson's Approach to Renormalization Theory", I gathered the impression that in the Wilsonian approach, one starts by analyzing ...
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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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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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1answer
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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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1answer
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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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1answer
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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 $O_i$ ...