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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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1answer
435 views

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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472 views

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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1answer
285 views

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
312 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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33 views

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 ...
3
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0answers
79 views

Local Effective actions

While studying partition functions in general, i came across a statement which says that "the partition function of a theory without gapless excitations must be a local functional of the background ...
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157 views

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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185 views

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}+...
3
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2answers
135 views

Does the Flavor symmetry forbid $uu\rightarrow cc,ss$?

This question comes from the reading of this paper. They suppose a flavor symmetry group $G_F = U(3)_q\times U(3)_{d} \times U(2)_{d}$ which acts on the three LH quarks $q_L$, three RH quarks $u_R$ ...
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128 views

For intersecting branes, are we allowed to compactify on a torus such that one of the branes becomes dense in it? What is the result?

The story of how to get chiral fermions in the low-energy effective theory of a string theory with intersecting branes goes something like this: At the point of intersection of two branes, a direct ...
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269 views

Integrating out heavy fields while preserving symmetries

The basic a-b-c for integrating out heavy fields what one learns when making the example of Fermi theory, is that if you have a Lagrangian $L= -\frac{1}{4}F^{\mu\nu}F_{\mu\nu}+\frac{1}{2}M^2 V^\mu V_\...
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1answer
321 views

What is the problem with quantizing GR in the Effective Field Theory approach?

In the modern view due to Wilson, the cut-off $\Lambda$ is an intrinsic property of a theory and renormalization just means that the theory is invariant under scale transformations below $\Lambda$. ...
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1answer
759 views

Uses of effective action and effective potential

Effective potential allows us to answer the question that whether there will be spontaneous symmetry breaking induced by quantum corrections. Is there any other information that can be extracted from ...
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2answers
385 views

Top quark mass $m_t$ at energy scales $\mu < m_t$?

Edit - Maybe formulated differently: Does it make sense to talk about the top mass at energies below $m_t$, although in all processes the corresponding energy scale is above $m_t$, because of the rest ...
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1answer
56 views

Why is it legitimate using bispinors in HQET?

I am reading about HQET in Grozin's book http://www.amazon.es/Effective-Theory-Springer-Tracts-Physics/dp/3540206922. While constructing the Lagrangian he first consider the usual QCD Lagrangian with ...
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1answer
185 views

Chiral current VEV below the QCD scale

Let's have pure QCD. I know that after spontaneous symmetry breaking quark bilinear form are replaced by their averaged values: $$ \bar{q}_{i}q_{j} \to \langle \bar{q}_{i}q_{j}\rangle \approx \Lambda_{...
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116 views

Symmetry of interaction lagrangian and symmetry of full lagrangian

Suppose we have lagrangian $$ \tag 1 L = \frac{\theta}{f_{\gamma}}F_{EM}\tilde{F}_{EM} +\frac{1}{2}(\partial_{\mu}\theta)^2 - \frac{1}{2}m_{\theta}^2\theta^2 + L_{SM}, $$ where $\tilde{F}_{EM}$ ...
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Vector mesons as background gauge fields

Suppose we have some complicated fundamental theory of fermions and gauge fields which involves global chiral symmetry and global anomalies which breaks some subgroup of this symmetr. At some energy ...
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1answer
448 views

Wilsonian Renormalization Group and Symmetries of the EFT

I have am action $S_0$ valid up to energy scale $\Lambda_0$ with renormalisable terms. I want to study the EFT at a lower scale $\Lambda \ll \Lambda_0$, by using the Wilsonian RG. It will give me an ...
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70 views

Baryon effective Lagrangian

I'm trying to understand how to construct effective lagrangians for the hadrons. I understand the procedure for the mesons but I get stuck on baryons. In particular I don't understand how the baryons ...
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1answer
428 views

Could string theory be an effective theory?

I know that many quantum field theories could be low-energy effective theories in String Theory (ST), but I've also read and heard that ST cannot itself be an effective theory. I suppose this has ...
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2answers
124 views

What justifies the perturbative expansion in chiral perturbation theory?

The Lagrangian of chiral perturbation theory is ordered following a momenta power counting scheme, having terms at leading order (which is two 2 $O(p^2)$) next to leading order ($O(p^4)$) and so on. ...
3
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1answer
103 views

Effective theories and unbounded operators

If you have two operators, one the true Hamiltonian $H$ and one we call an effective Hamiltonian $H_{eff}$ and say they agree on every eigenvector with eigenvalue up to $E_{eff}.$ Above that, they can ...
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62 views

How is (if it is) gauge symmetry realized in chiral perturbation theory?

I often read that an effective field theory must have the symmetries of its UV completion. Chiral perturbation theory is an Effective Field Theory (EFT) of QCD. I know that the approximate chiral ...
5
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1answer
190 views

Can the effective vertex for $\gamma\to3\pi$ be derived directly from the anomaly?

My question is whether the effective vertex for $\gamma\to3\pi$ can be derived directly from the anomaly (given in the first equation below), in analogy with the $\pi^0\to2\gamma$ vertex? As far as I ...
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1answer
129 views

A pedagogical exposition of the hadron physics?

I am looking for a textbook/lecture notes/etc. on the basics of hadron physics. I wish to understand how to construct the effective Lagrangian for pions and nucleons starting from the QCD Lagrangian. ...
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1answer
492 views

Redefinitions of Lagrangians using EOM

I am trying to understand an statement of this paper. In section 2 this Lagrangian is introduced $$\mathcal{L}_4=-|D_{\mu}\phi|^2-\lambda_{\phi}|\phi|^4-\frac{1}{4g^2}F_{\mu\nu}^2\qquad{}\mathcal{L}...
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Where do negative powers of $f_\pi$ in the hadronic amplitudes come from?

According to Peskin and Scrhroeder the pion decay constant $f_\pi$ is defined via the following matrix element $$\left\langle0|j^{\mu5a}(x)|\pi^b(q)\right\rangle=-if_\pi \delta^{ab} q^\mu e^{-iqx}$$ ...
3
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1answer
220 views

Doubts with basic renormalization

When we renormalize to obtain the physical mass, the $\Lambda$ dependence of the physical mass is removed by introducing the counterterms in the Lagrangian. So whether we put $\Lambda\rightarrow\infty$...
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741 views

Scattering amplitude, link between quantum mechanics and QFT

In quantum mechanics, we can define the scattering amplitude $f_k(\theta)$ for two particles as the magnitude of an outgoing spherical wave. More precisely, the asymptotic behaviour (when $r\...
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182 views

How can we see that a 4D N = 2 sigma model will yield a 3D N = 4 sigma model when compactified on a circle?

I have a question about sigma models in 3D. If we have $\mathcal{N}=2$ field theory on $\mathbb{R}^4$ and compactify it on $\mathbb{R}^3 \times S^1_R$ (in which $S^1_R$ is a circle of radius $R$) we ...
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1answer
203 views

Magnetic moment in four-fermion theory

I'm trying to calculate the neutrino magnetic moment in the theory with this additional term in the Lagrangian: $\frac{a}{M^2}(\bar{\nu}\sigma_{\mu\nu}\nu)(\bar{e}\sigma^{\mu\nu}e)$, where $\sigma^{\...
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1answer
310 views

Effective field theory (EFT) and Renormalizability

Was trying to understand renormalizability in EFT. This is a little confusing especially the part of the misnomer. Can someone please explain this? Text taken from Wikipedia: "However, in an ...
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0answers
105 views

Matrix elements of four-quark operators [closed]

In weak interaction phenomenology, especially in strangeness changing processes, effective four-quark operators are used. Such as $Q_1 = (\bar{s}_\alpha \gamma_\mu (1-\gamma_5) d_\alpha) (\bar{u}_\...
2
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0answers
108 views

Effective field theory of inflation in the slow roll case

I'm reading this set of notes by Daniel Baumann on the effective field theory of inflation but I can't quite understand one step in section 3.1.1 concerning slow roll inflation. Basically, the author ...
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1answer
253 views

Why don't we have logarithms or exponentials of the fields in the Lagrangians?

All the Lagrangian densities I have seen have always been polynomials of the fields. Is this a coincidence or is there a reason which forbids, say, Lagrangians with logarithms or exponentials of the ...
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0answers
99 views

Recommendation about higher derivative theory

Are there some textbook or review about following parts of higher derivative Lagrangian? How to figure out the degrees of freedom of higher derivative theory? How to analyse the stability of a ...
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0answers
202 views

Non-Hermitian Lagrangian in Quantum Field Theory

I have seen more than once non-Hermitian Lagrangian densities being used in effective field theories. Usually the problem of unitarity is explained away with decays into some degree of freedom not ...
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340 views

Weinberg's QFT and superconductors

In the beginning of subparagraph about superconductors (which corresponds to paragraph about spontaneously symmetry breaking) Weingberg states that in superconductors EM gauge invariance is ...
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70 views

Does graviton loops affect the seperately covariant conservation of energy momentum of two noninteracting sectors of matter

Consider the action $$\int \sqrt{-g}\left[R[g]+\mathcal{L}_{m1}(g,\psi_1)+\mathcal{L}_{m2}(g,\psi_2)\right]$$ Classically we have $$\nabla^\mu T^1{}_{\mu\nu}=0,\,\,\,\,\nabla^\mu T^2{}_{\mu\nu}=0$$ ...
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175 views

Computing things in Effective field theory

I find it hard to go through most of the homework problems in an effective field theory course. In fact I think I have developed a general disdain in solving hard Quantum field theory related problems....
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278 views

Understanding the effective low-energy Lagrangian for hadrons

My course in Higgs Physics is discussing a two-nucleon low-energy effective theory of hadron interaction. With $\psi=(p,n)$, the pion is defined as $\vec{\pi}= i \bar{\psi}\vec{\tau} \gamma_5 \bar{\...
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0answers
150 views

Hamiltonian Operator for nonrenormalizable Effective Field Theories?

Assuming we have a Effective Field Theory, for example a Real Scalar Field Theory, defined through a Lagrangian density of the form $\mathcal{L}_{eff} = \frac{1}{2}\partial_\mu\phi \partial^\mu\phi - ...
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499 views

Effective Field Theory (EFT) decoupling top

The decoupling theorem of Appelquist-Carazzone says that if you want to decouple a particle, the low energy resulting theory need to be renormalizable. You can't do that for the top, because you break ...
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1answer
112 views

Effective field theory for fermion gas

Reading about fermion gas in a paper they used the following Lagrangian, which describes an effective field theory for nonrelativistic fermions (I neglect the four point interaction term). $$ L = \...
8
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2answers
413 views

Naive questions on the concept of effective Lagrangian and equations of motion?

Let us consider a LC circuit containing an electric dipole moment, the quantum system (electric field $E$ coupled with a dipole moment) can be described by the path integral $$Z=\int DEDxe^{i\int dtL},...
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1answer
1k views

Coleman-Weinberg potential: resum at 2 loops?

Say we want to compute the Coleman-Weinberg potential at 2 loops. The general strategy as we know is to expand the field $\phi$ around some background classical field $\phi \rightarrow \phi_b + \phi$...
8
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2answers
627 views

Why does the Walecka model not include pions?

The Walecka or $\sigma$/$\omega$-model is an effective theory describing nucleon-nucleon interaction by an exchange of $\sigma$/$\omega$-mesons. Why does it not include interactions by pions?
8
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1answer
211 views

What is a superfluid in field theoretic terms?

I'm wondering how one precisely defines a superfluid in terms of the effective field theory description. In Nicolis's paper http://arxiv.org/abs/1108.2513 there seems to be an extremely simple ...