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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43 views

A bit of confusion with central idea of “running” coupling constants

An effective quantum field theory of a single scalar field $\phi$ is described by an action, $S(\phi,\{g_n\})$ where $\{g_n\}$ denote the coupling constants of the theory. The corresponding path-...
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Wilson's approach to renormalisation according to Peskin & Schroeder

Although Peskin & Schroeder treats Wilson's approach to renormalisation theory in some depth, I don't get one of its main points. According to P&S (p.401): Imagine that we wish to compute ...
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Terms that appear in the RG flow with regards to symmetries of the Lagrangian

Consider a theory with Lagrangian $\mathcal{L}$ with a global $U(1)$ symmetry, and consider adding a deformation $$\mathcal{L}_g = g \mathcal{O}(x)$$ which breaks the $U(1)$ symmetry explicitly. ...
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What is an effective field theory (EFT)? Is the standard model (SM) an EFT? Till which scale? How is included gravity?

What is an effective field theory (EFT)? and why all the observable interactions until one scale are only a finite number that we know? Is the standard model (SM) an EFT? till what distances? I real "...
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Baryons in flavor $SU(N)$ (in ChPT)

For flavor $SU(2)$ (Isospin) we have two $\frac{1}{2}^+$ baryons, the nucleons. For flavor $SU(3)$ we have the eight baryons in the octet. In a world with $N$ light quarks we would see a baryon ...
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Does the Darwin Lagrangian neglect deviations from the Coulomb field?

The Darwin Lagrangian is said to describe the interaction between two charges to order $(v/c)^2$, and consists of a free part $$L_0 = \sum_{i = 1, 2} \frac12 m_i v_i^2 + \frac{1}{8c^2} m_i v_i^4$$ and ...
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Amplitude of an operator in BSM physics

I am currently working on effective field theory within the standard model (SMEFT). In this formalism, one introduces higher dimensional operators to the standard model Lagrangian, typically operators ...
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Renormalization in effective field theory [closed]

I have tried to solve these two questions. I have read different papers and textbooks in order to get an answer but all effort proved abortive. Someone should kindly assist in these equations.
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When is Schwartz's method for “integrating out” a field valid?

In Schwartz's QFT book, heavy fields are often "integrated out" by simply solving their equations of motion formally (i.e. allowing things like $\Box^{-1}$) and plugging them back into the Lagrangian. ...
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Where can I find Hollowood's lecture notes on cutoffs and continuum limits?

I'm trying to find a copy of Tim Hollowood's "Cutoffs & Continuum Limits: A Wilsonian Approach to Field Theory". These are unpublished lecture notes that I've seen dated to 1998 or so, and have ...
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Deriving the beta function with the Wilson way

I want to derive the beta function of a theory ( do not matter which one ) with the Wilson way of doing, i.e. by integrating out modes between $b\Lambda$ and $\Lambda$, $b<1$. For the $\phi^4$-...
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Calculating higher-derivatives of quantum effective potential (Weinberg QFT chapter 16 problem 2)

Couple a set of classical currents, denoted by $J$, to a set of fields $\phi$. Let $iW[J]$ be the sum of all connecte vacuum-vacuum amplitudes. The Weinberg Quantum Theory of Fields chapter 16 says ...
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Effective action for ferromagnetism and ferroelectricity

In Three Lectures On Topological Phases Of Matter section 2.1 mentioned, that: $$ I^\prime = \int dt d^3x \; \left(\vec{a}\vec{E}+\vec{b}\vec{B}\right) $$ correspond to ferromagnetism and ...
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106 views

New Physics contributions to the Wilson Coefficients

In this article (arXiv:1507.06660v1 [hep-ph]), the authors tried to extend the SM by adding a new sector, consisting of vector-like quarks and leptons $Q$, $L$ and two scalars $\phi$, $\chi$. They ...
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Higgs mechanism and spontaneous symmetry breaking

I'm really confused about spontaneous symmetry breaking and the Higgs mechanism. I've searched for other answers but I couldn't still resolve all my doubts. I also understand that I'm asking a lot of ...
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Calculating the pion decay constant in Chiral Perturbation Theory

I am trying to calculate the pion decay constant by following this paper [arXiv]. Since the decay constant is defined via $$ \langle 0| A_\mu (0) | \phi(p)\rangle = \text{i} p_\mu F_0 \tag{3.19}$$ ...
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Polchinski's toy model of renormalization group flow: significance of main steps

In "Renormalization and Effective Lagrangians" (Nucl. Phys. B, 231 p269, 1984; preprint), Polchinski begins section 2 with a toy model to demonstrate the renormalization group with a relevant and ...
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Marginal Operator, Kinetic Term, Effective Field Theory (EFT) [closed]

Is the kinetic term of an effective field theory always marginal by definition?
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Are Yukawa interaction theories still in use?

As is commonly known, the Yukawa interaction (scalar/pseudoscalar) was used to describe the old-school, pion mediated, strong force, long before the discovery of quarks. The theory has been proven to ...
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Correlation functions under rescaling

I was reading this lecture note on Wilson's renormalization group and have hit a snag. I can't obtain equation 5.22. I tried to do the following: \begin{equation} \Gamma^{(n)}_{s\Lambda}(sx_1,…,sx_n;...
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Why is technical naturalness a natural expectation?

In first few minutes of this lecture by Nathaniel Craig, he explains the idea of Dirac naturalness in the following way. Let us consider a QFT as an effective theory with a UV cut-off $\Lambda$. Let $...
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Effective $T$ matrix in Kondo Hamiltonian

Consider the Kondo Hamiltonian $$H=\sum \epsilon_k c^\dagger_{k\sigma} c_{k\sigma} + J^z S^z \sum c^\dagger_{k'\alpha} \sigma_{\alpha\beta}^z c_{k\beta} + J^{\pm} \sum \left( S^+ c^\dagger_{k',-} c_{k,...
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Quantum effective action/potential in effective theories defined on a coset space

The textbook derivation of the quantum effective action (see e.g. Weinberg, vol. 2, sec. 16) and its energy interpretation seems to require that the fields take values from a linear space, as it ...
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Renormalization and fluid dynamics

Both Quantum Field Theory and fluid dynamics rest upon discarding finer details of the system and/or small-scale degrees of freedom. I understand that both frameworks require such removal ...
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Higher dimensional operators in Srednicki's EFT

In Mark Srednicki's QFT book in chapter 29, page 187 he talks about the leading contribution of $c_{d,i}$ being given by a 1-loop diagram with 2n external lines representing $|k| < \Lambda$ momenta,...
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The importance of dimensions in the effective Lagrangian

I would like to examine the contributions from the new physics in any process in particle physics with the help of the Effective Lagrangian method. In this method, the standard model Lagrangian plus ...
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Do we care about CFTs in particle physics?

This question is related to these others: mostly this one, but also this one and this one. Do we care about CFTs in particle physics? Let me explain. Suppose we don’t know anything about string ...
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Fierz identities to eliminate all vector and tensor Dirac matrices in effective operator (Weinberg)

In the paper titled "Baryon- and Lepton- Non-conserving processes" (prl, 1979) S. Weinberg used operator formalism in effective field theory to analyse beyond the standard model processes which ...
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Effective action for 1D anti-ferromagnet

I'm following Fradkin's (p. 204) derivation of the effective action for a 1D anti-ferromagnet. He splits the spin field $\vec{n}$ into two pieces - a slowly varying $\vec{m}(j)$ which is the order ...
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Effective exapsnion of Brans-Dicke like gravity

I'm working on the effects of higher derivative terms in gravitational theories and I have a question based on the effective expansion of a Brans-Dicke-like theory. Essentially my question is, in my ...
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Heirarchy problem

Can anyone explain the hierarchy problem in context to Higgs mass corrections by scalar loop and fermion loop (the problem arising when we try to treat SM as an EFT)? and how do these corrections ...
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Feynman rules for space-dependent coupling

Let's say I have an effective action which looks like (I got this action from large $N$ method for $\varphi^4$ theory): $$\int \frac{d^4x}{2g}\phi^2(x)+\int d^4x \ \log(-\nabla^2+\mu^2+i\phi(x)). $$ ...
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Projecting out interactions with high-energy states

I have a single-particle Hamiltonian with a discrete energy spectrum $E_{n,k}$ with two degrees of freedom, $n=0,1,2,3...\infty$ and $k$ which has only a few possible values. $E_{n,k_1}$ and $E_{n,k_2}...
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Where the derivative corrections come from in Wilson renormalization?

I known that in the Wilson renormalization process fast modes are integrated out in order to define an effective action for the low modes field. Considering phi to the fourth theory it's easy to see ...
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Antisymmetric matrices in effective field theory

I'm trying to construct a nonlinear $d$-dimensional version E&M as an effective field theory. Let $F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu$ be the field strength. The most general action ...
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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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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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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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How is the chiral condensate estimated from the pion decay constant?

In low-energy QCD, there are several dimensionful quantities that come up. Writing the chiral condensate as $$\langle \Omega | \bar{q}_{Ri} q_{Lj} | \Omega \rangle = - v^3 \exp \left(\frac{2 i \pi^a(...
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Renormalisation group flow of the $\phi^4$ theory

I am reading Peskin & Schroeder about the renormalisation group flow of the $\phi^4$ theory: $${\cal L} = \frac{1}{2}(\partial_\mu\phi)^2 +\frac{1}{2}m^2\phi^2 + \frac{\lambda}{4!}\phi^4 $$ P &...
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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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IIB Supergravity from worldsheet (super)conformal invariance of Green-Schwarz string

After reading this question How are low energy effective actions derived in string theory? I began to wonder what is the coupling of the string to the other sugra fields. In almost all textbooks ...
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Are Instantons Massless?

That is, are the only field configurations which give a non-zero winding number ones in which the Fourier transform includes a factor like $\theta(k^0)\hat{D}\delta(k^2)$, where $\hat{D}$ is some ...
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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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Piecewise solution to Euler-Lagrange equations in effective field theory

I would like to consider a background for a quantum field theory made up by connecting continuously two different solutions of the Euler Lagrange equations. The problem is one dimensional (let's call ...
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438 views

Is Hilbert-Einstein action just the leading order of some kind of series?

Introducing the action for the gravitational field my GR professor stated that, in principle, one could write it as $$S = k\int d^4x\sqrt{g}(\sum_n\sum_m a_{nm} R_n^m - 2\Lambda), \space \space \...
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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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339 views

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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59 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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2answers
78 views

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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