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0answers
15 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 ...
0
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0answers
41 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 ...
0
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0answers
19 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
163 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
59 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 ...
3
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2answers
122 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 ...
-1
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1answer
106 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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0answers
26 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
26 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, ...
7
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0answers
96 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
75 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 ...
4
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0answers
61 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 $\tilde{F}_{EM}$ ...
2
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0answers
38 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
votes
1answer
157 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 ...
1
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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 ...
0
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0answers
25 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 ...
8
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1answer
295 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
74 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
64 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
24 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
votes
1answer
63 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
votes
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
130 views

Redefinitions of Lagrangians using EOM

I am trying to understand an statement of this paper. In section 2 this Lagrangian is introduced ...
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 $$\left\langle0|j^{\mu5a}(x)|\pi^b(q)\right\rangle=-if_\pi \delta^{ab} q^\mu e^{-iqx}$$ ...
2
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1answer
123 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 ...
4
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0answers
211 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 ...
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0answers
68 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
votes
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 ...
3
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0answers
56 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) ...
1
vote
0answers
110 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 $$ ...
2
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0answers
51 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
50 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
103 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
98 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 ...
1
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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
154 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 ...
3
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0answers
137 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 ...
5
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0answers
89 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
283 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 ...
1
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1answer
83 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
votes
2answers
281 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 ...
10
votes
1answer
624 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 + ...
8
votes
2answers
306 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?
6
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0answers
106 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 ...
3
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1answer
243 views

Renormalizability of standard model

I'm wonder what precisely is meant by the renormalizability of the standard model. I can imagine two possibilities: The renormalizability of all of the interaction described by the Lagrangian before ...
4
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1answer
114 views

Quantum field theory defines its own bounds of applicability

I recall hearing in a lecture something along the following lines: "Due to some intrinsic feature of quantum field theory in general (or maybe it was the standard model?), we know where it is ...
3
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2answers
156 views

What is the logic of not regarding perturbative renormalizability as a fundamental requirement?

I read a statement in Becker and Becker's String Theory and M-Theory page 2. After pointing out the non-renormalizablity of GR by the dimension of gravitational constant, it is said: Some ...
2
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1answer
214 views

NRQCD: Why are quarks and anti-quarks treated independently?

I am studying these lectures on effective field theories and I am having some problems to understand how the Non-Relativistic QCD (NRQCD) Lagrangian is constructed. This theory is often used to ...