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30 views

A few questions concerning one loop corrections to the action

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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0answers
97 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}+...
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1answer
63 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 $u_R$ ...
4
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0answers
54 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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0answers
43 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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0answers
21 views

Pion decay from chiral anomaly

I have to compute the decay rate of the process: $$ \pi^{0} \rightarrow \gamma \gamma $$ with 4-momenta $P \rightarrow K_{1}+K_{2},$ by the means of the following effective Lagrangian, coming from ...
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0answers
54 views

Pion-pion scattering amplitude with an effective Lagrangian

I have to compute the scattering amplitude at tree level for the process $$ \pi^{a}\pi^{b} \rightarrow \pi^{c}\pi^{d} $$ with an interaction given by what is written in the square brackets of the ...
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0answers
22 views

Resummation of large logarithms in effective field theory

I am trying to learn about the ideas of large-logarithms in effective field theory from a set of notes. However the following paragraph is confusing me: This doesn't seem quite right to me. Surely ...
3
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1answer
168 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 $\Lambda$. ...
3
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1answer
82 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 ...
4
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2answers
143 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
108 views

Can Quantum Field Theory be right even though it doesn't include gravity? [closed]

Quantum Field Theory doesn't include gravity, so does that mean it can't be right?
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32 views

Effective medium approaches - Volume averaging vs homogenization?

In dealing with multiphase two phase systems as an effective medium there are two approaches that can be taken. Volume averaging and homogenization. Volume averaging is very intuitive, just take ...
2
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1answer
35 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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0answers
28 views

The question about codimension of fixed point and about irrelevant operators

Recently I've read about Wilsonian renormalization group (WRG) in context of condensed matter phase transitions. The important concepts of WRG are fixed points and type of operators (eigenvalue, ...
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105 views

Mean Field Theory vs. Effective Field Theory

I am reading my many-body quantum physics textbook, and specifically the section on Mean field theory. It seems that the Mean field approximation in the Hamiltonian formalism must be equivalent to "...
2
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1answer
76 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_{...
4
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0answers
67 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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39 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 ...
3
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1answer
183 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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0answers
41 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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0answers
26 views

Effective Medium

Please consider the following problem : A plane wave of wavenumber k is incident on an infinite slab which is inhomogeneous in the z direction. Also assume harmonic time dependence and that the ...
10
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1answer
328 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 ...
2
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2answers
79 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. ...
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0answers
20 views

Do operator bases in Lagrangians have a vector space structure?

In effective field theories we deal with bases of operators. I wonder in which sense is this similar to bases of a vector space. We can change bases and write the Lagrangian in another basis, just as ...
3
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1answer
67 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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0answers
27 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 EFT of QCD. I know that the approximate chiral symmetry of QCD is realized ...
3
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1answer
65 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 ...
3
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1answer
58 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. ...
3
votes
1answer
137 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}...
5
votes
1answer
86 views

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
126 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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221 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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0answers
69 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 ...
4
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1answer
109 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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0answers
60 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}_\...
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0answers
122 views

Nature of the Wess-Zumino term in an effective field theories

Let's have theory involves fermions which interact through spontaneously broken (by field $g = ve^{i\theta }$ value $v$) $U(1)$ group, and then to integrate fermions out. Will Wess-Zumino term $$ \...
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0answers
57 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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0answers
53 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 ...
4
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0answers
108 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 ...
2
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0answers
108 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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0answers
58 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 $$\nabla^\mu T^1{}_{\mu\nu}=0,\,\,\,\,\nabla^\mu T^2{}_{\mu\nu}=0$$ ...
3
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0answers
155 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....
3
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0answers
144 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
91 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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0answers
300 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
84 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 = \...
7
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2answers
298 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
656 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
321 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?