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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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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379 views

Finite quantum gravity?

I'm working through an article that has some questionable assertions. The article is by Frank Tipler, "The structure of the world from pure numbers". (I'm going to ignore the fact that some of Tipler'...
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168 views

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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713 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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190 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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145 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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126 views

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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109 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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96 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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129 views

Energy interpretation of 1PI effective potential in Weinberg 16.3: is adiabatic turning on the current necessary?

In section 16.3 of Weinberg, he interprets the 1PI effective potential as the minimum of expectation value of the energy density under some constraint. The essential argument is \begin{equation} \...
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43 views

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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61 views

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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79 views

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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129 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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123 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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99 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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174 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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275 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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42 views

Wavefunction Renormalization in Wess-Zumino Model

In Modern Supersymmetry: Dynamics and Duality, on page 134 and 135 in section 8.2, the authors studied the wavefunction renormalization of the Wess-Zumino model. The kinetic terms are given by $$\...
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149 views

How do Graviton-based theories of gravity explain the expansion of the universe?

In General Relativity, the expansion of the universe is modeled using the Friedmann–Lemaître–Robertson–Walker metric, and the expansion itself is a metric expansion by which the scale of space itself ...
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37 views

Non-trivial content of AdS/CFT for a generic EFT on AdS

I have a very generic and naive question on the actual content (and usefulness) of the AdS/CFT conjecture in the low energy approximation where one considers a low energy QFT on AdS, comprising ...
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33 views

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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1answer
55 views

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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68 views

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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258 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
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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62 views

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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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 ...
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181 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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107 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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335 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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313 views

Effective Field Theories of QCD

Recently, I am studying the online course Effective Field Theory provided by MIT OCW. Prof. Stewart gives a nice picture to summarize the effective theories: As a newbie in this field (I only have a ...
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60 views

Marginal interactions for Fermi surfaces

I am struggling to understand Polchinski’s derivation (https://arxiv.org/abs/hep-th/9210046) of the conditions for marginality of the 4-fermi operator. For a scattering process $(\mathbf{p}_1,\mathbf{...
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39 views

Size of quantum corrections at infinity

Suppose we have a one dimensional field theory for the field $\phi(r)\;r\in[0,\infty]$ and that the solution for the background (Euler Lagrange equations) give a function $\phi_0$ that goes to a ...
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62 views

Effective Lagrangians

I get the impression from reading, e.g., this paper, that the term "effective Lagrangian" refers to a Lagrangian derived from a Taylor series expansion of an arbitrary function of known invariants. ...
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48 views

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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46 views

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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61 views

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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46 views

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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87 views

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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39 views

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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46 views

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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104 views

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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23 views

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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45 views

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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90 views

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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166 views

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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111 views

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
96 views

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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32 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 ...