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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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Time dependent mass terms in field theory

In my research on Q-balls (a certain type of non-topological soliton) in cosmological backgrounds, I have obtained an equation that is nearly usable, except for one caveat. It would require me to ...
Daniel Waters's user avatar
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What does it mean to "resum" the large logarithms?

I am struggling to understand the concept of resummation of large logarithms in QFT; from what I learnt so far the problem relies on the fact that if a full theory defined in the UV contains much ...
Filippo's user avatar
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How do I obtain the low energy supergravity actions from the 5 superstring theories?

In Domain-Walls and Gauged Supergravities by T.C. de Witt, there is a small table giving the 5 string theories and each of their effective sugras. I am looking for detailed reviews of how these sugras ...
bradas128's user avatar
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Weyl variation of a generic action

In this paper https://arxiv.org/abs/hep-th/9906127 (see eq. 15) The following identity appears $$ \delta_{W} \int d^d x \sqrt{-\gamma} \tilde{\mathcal{L}}^{(n)} = \int d^d x \sqrt{-\gamma} \sigma\left(...
Faber Bosch's user avatar
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Uniqueness of Maxwell Lagrangian: Why does it not include the term $c_3 (\partial_\mu j_\nu)F^{\mu \nu}$?

In the textbook Condensed Matter Field Theory by Altland and Simons, it is said that the Maxwell Lagrangian $\mathcal{L}$ coupled to a four-current $j^\mu$ satisfying $\partial_\mu j^\mu = 0$ is the ...
zeroknowledgeprover's user avatar
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Why does integrating out microscopic degrees of freedom lead to the effective free energy rather than the effective energy?

In David Tong's lecture notes on statistical field theory, he considers the partition function of the Ising model and computes the effective free energy by integrating out the microscopic details of ...
VinV's user avatar
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Fermi theory cutoff from unitarity bound

Tree-level cross sections for processes described by Fermi theory behave like $\sigma $ $\sim$ $G_{F}^2 \cdot s$, where $G_{F}$ is the Fermi constant and $\sqrt s$ is the energy entering in the ...
onibaku's user avatar
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The origin of the Hierarchy Problem

In the answer to this question on the origin of the hierarchy problem, it is stated that: The low-energy parameters such as the LHC-measured Higgs mass 125 GeV are complicated functions of the more ...
tomdodd4598's user avatar
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Loops and UV divergences

I read when asked whether a force could only exist at a certain phase transition or high energy: "I am not aware of a coupling that only exists at high energies or in a phase transition -- in ...
Jtl's user avatar
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Why the coupling constant in context of different approaches has different energy dependence?

I know that in the language of renormalization group, the coupling constant in the Hamiltonian is dependent of energy, for example in condensed matter physics, of band width. So, we can do a 'poor man'...
Houmin Du's user avatar
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3-Particle Kinematics and Parity of Operators

Recall that if the momentum of scattering amplitudes is taken to be complex and from little group scaling that the 3-particle interaction for massless particles of any spin is given as \begin{equation}...
MathZilla's user avatar
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Chern-Simons (K matrix) theory and ${\rm Spin}^{\mathbb C}$ connections

If I understand correctly (e.g. from this paper), an Abelian bosonic Chern-Simons theory defined on $T^2\times \mathbb R$ is specified by a $K$ matrix via e.g. $S \sim \int_M K_{IJ}A^I \wedge dA^J$. ...
Joe's user avatar
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Invert operator to integrate heavy fields

We have a Lagrangian $$\mathcal{L}=\frac{1}{2} \partial_\mu \Phi \partial^\mu \Phi - \frac{1}{2} M^2 \Phi^2- \frac{\lambda}{4}\phi^2 \Phi^2 - \frac{g}{2} \Phi \phi^2+\cdots $$ where $\Phi$ denotes a ...
Newstudent's user avatar
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Why do we rescale momenta after integrating out high momenta in Wilsonian renormalization?

In Section 12.1 of Peskin & Schroeder they motivate Wilson's approach to renormalization by asking how a quantum field theory changes after changing the momentum scale. To answer this they start ...
CBBAM's user avatar
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Derivative interactions in the Wilsonian renormalisation Group

I am currently working through some basic renormalisation group problems, and have come to one about derivative interactions. It has been a while since I have studied QFT formally so bear with me ...
Aidan's user avatar
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Why don't we include diagrams with fermion and gauge boson external lines while calculating the effective potential of Standard model?

While calculating the effective potential of Higgs boson, we aim at $V_{eff}(h)$ instead of $V_{eff}(h, W^{+}, W^{-}, Z, quarks, leptons)$. I think the true vacuum should be the minimum of this ...
Bababeluma's user avatar
3 votes
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What is the physical meaning of the counterterms we add in Lagrangians?

I have a probably very silly question. Please help me with it: Say we consider the QCD Lagrangian. All of it's terms involve various fields. Now this Lagrangian can simply be called the Lagrangian of ...
SX849's user avatar
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Reference request scale anomaly

Can anyone recommend some books, notes and review-oriented papers on scale anomaly, with a view towards its relation to renormalization? Such as an anomaly perspective on RG, Callan-Symanzik equations ...
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What is the interpretation of the $\beta$ and $\gamma$ functions in the renormalization group?

Let $M$ be a renormalization/momentum scale, $\lambda$ a coupling, $G^{(n)}$ the $n$-point Green's function, $Z$ the field strength, and $\Lambda$ a momentum cutoff. When studying the renormalization ...
CBBAM's user avatar
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Renormalization group equation, the Callan-Symanzik equation, and renormalization group flow

I am learning about the renormalization group and I am getting confused on some terminology. For the massless $\phi^4$ theory the Callan-Symanzik equation is: $$\big[ M \frac{\partial}{\partial M} + \...
CBBAM's user avatar
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Is the magnitude of the $\beta$ function important?

I am currently studying the renormalization group in quantum field theory and have gotten up to computing the $\beta$ function perturbatively . While I only have a basic understanding of it so far, ...
CBBAM's user avatar
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1 answer
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Problem solving for Wilsonian Effective Action

I'm currently doing some basic questions on renormalisation group, but I've ran into a wall when it comes to one particular step in an answer. The question is as follows: This problem is a toy model ...
Aidan's user avatar
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Triviality of $\phi^4$ theory, is it settled now (2024)?

According to the answer on question 364576 this should be settled. But after looking for clear statements of the current situation on triviality of $\phi^4$ theory, I'm still not sure, because: In ...
Jos Bergervoet's user avatar
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1 answer
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Question about RG from QFT perspective, in particular Weinbergs book

This must be fairly basic I fail to understand. According to Weinberg, QFT Vol2, Ch.18 (The preamble) When we replace bare couplings and fields with renormalized couplings and fields defined in terms ...
Confuse-ray30's user avatar
5 votes
1 answer
205 views

Wilsonian RG in QFT: what is the difference between renormalized and bare couplings?

I want to understand the relation between the Wilsonian RG and the usual QFT RG approach. Several questions have been asked, such as this and many others, yet I don't find a conceptual answer to what ...
Mr. Feynman's user avatar
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Why are the corrections to the effective Lagrangian (Wilsonian renormalization) given by connected diagrams only?

This question will fully refer to the presentation ref. 1, from which I'll take the numbering. Since it involves also diagrams and it appears as a fairly basic question about Wilsonian renormalization,...
Mr. Feynman's user avatar
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Why are these terms not present in the QED Lagrangian?

I am working though some questions for my QFT/ QED exam and i am having trouble with the following question: Explain why the following terms cannot be part of the Lagrangian of QED: $-g(\bar{\psi}\...
ugur's user avatar
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Quantum effective action for Yang-Mills theories

During a course I came across a formula for the quantum effective action of a Yang-Mills theory in euclidean space and it appears like this (some indices may be dropped but I hope that won't be a ...
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1 answer
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Low-energy string effective action valid for large dilaton field?

The low-energy effective action of the bosonic string in the critical dimension $D=26$ is given by: $$S=\frac{1}{2\kappa_0^2}\int d^{26}x\sqrt{-G} \left[ \phi^2\left( R-\frac{1}{12}H_{\mu\nu\lambda}H^{...
John Eastmond's user avatar
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What is the definition of the 0th element of the spin 1/2 four vector?

Is it: $$ S_\mu = (I, \frac{1}{2}\vec{\sigma})\quad\text{or}\quad S_\mu = (0, \frac{1}{2}\vec{\sigma}) $$ Specifically in the "CHIRAL DYNAMICS IN NUCLEONS AND NUCLEI" Bernard,Kaiser,Meißner, ...
Alex Long's user avatar
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4-graviton vertex of which one is an emitting graviton

For a four graviton vertex function, suppose $h_{\alpha\beta}h_{\gamma\delta}h_{\varepsilon\zeta}h_{00}$, of which $h_{00}$ is the emitting graviton to infinity. Now if we associate four-momenta $p_1$,...
NovoGrav's user avatar
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0 answers
172 views

Is there any renormalization group with infinite number of generators that does not satisify a renormalization group equation?

A generating set of a semigroup(monoid) is a subset of the semigroup set such that every element of the semigroup can be expressed as a combination (under the semigroup operation) of finitely many ...
XL _At_Here_There's user avatar
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$B$-field reducion in the Kaluza-Klein mechanism

Given the following $d+1$ dimensional dilaton-gravity-Maxwell low-energy effective action in the target space of a bosonic string: $$S=\frac{1}{2\kappa^2}\int d^{d+1}x\sqrt{-\tilde{G}}e^{-2\tilde{\Phi}...
Daniel Vainshtein's user avatar
1 vote
0 answers
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How scalar field couples to the $B$-field in Dilaton-Gravity-Maxwell action?

Given the following $d$ dimensional dilaton-gravity-Maxwell low-energy effective action in the target space of a bosonic string: $$S=\frac{1}{2\kappa^2}\int d^dx\sqrt{-G}e^{-2\Phi}\left[R-\frac{1}{12}...
Daniel Vainshtein's user avatar
1 vote
0 answers
76 views

What is the meaning of twist in OPE?

In Operator Product Expansion (such as explained in Peaking) there appear a quantity for an operator called twist, defined to be $d-s$ where $d$ is the scaling dimension of the operator and $s$ is it'...
Fabio Canedo's user avatar
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2 answers
122 views

What symmetry present in a low energy theory is broken or not exact at high energies?

The opposite is quite common such as EWSB, SUSY or GUT. Is there any example where a certain symmetry emerges from a low energy effective theory but is not present in the high energy theory?
user74750's user avatar
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3 votes
1 answer
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Exact RG as field redefinition

In Rosten's review of exact RG (arXiv:1003.1366), exact RG can be recast as field redefinition, but I don't see why it should be general discussion. Could you possibly explain to me why exact RG ...
HQMA's user avatar
  • 190
1 vote
1 answer
119 views

Contradiction in energy scales with regard to running coupling and observables

Here is the contradiction, which I arrive at. Renormalization group (RG) eqs. are basically a statement that observables (cross-section or Green's function) don't depend on the arbitrary ...
Sashwat Tanay's user avatar
6 votes
0 answers
108 views

How to reproduce the result of perturbative $\phi^4$ from exact RG

I am studying Exact RG and I have a question. I think, it should be possible to reproduce the flow equation of $\lambda_4$ term in perturbative RG, from exact RG. However, from Peskin, equation of $\...
HQMA's user avatar
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How does Schwinger get the QED effective action in source theory?

I'm reading Climbing the Mountain by Mehra, in which he explains Schwinger's source theory by an example. He appears to end up giving an explicit form for the effective action of QED and I don't ...
Kris's user avatar
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Difference between Bogoliubov-Shirkov renormalization group and Wilson's Renormalization group

I just learned the Wilsonian renormalization group from a QFT lecture, I heard that there is another renormalization group called Bogoliubov-Shirkov renormalization group which is a true group instead ...
Inuyasha's user avatar
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0 answers
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How to explain the reason of harmonic approximation by Wilson RG?

It's a part of my homework. In many body physics, considering the hamiltonian of the ions, we often use harmonic approximation then the hamiltonian turns to $$ H=\sum_{k}\hbar\omega(b^\dagger b+\...
Alex Chen's user avatar
3 votes
0 answers
77 views

Mismatch in the mass dimensions of the dilaton field

In chapter 7 of David Tongs' string theory lectures, the low-energy effective action of string theory is presented, and given by eq.(7.16): $$S=\frac{1}{2\kappa^2_0}\int d^{26}X\sqrt{-G}e^{-2\Phi}\...
Daniel Vainshtein's user avatar
4 votes
0 answers
109 views

What is the relationship between the renormalization schemes in quantum field theory and statistical field theory

Consider the $\phi^4$ theory for example. In QFT, we do renormalized perturbation theory by defining the theory at a particular scale, see for example, eq. 12.30 of Peskin and Schroeder: Then we can ...
TQFT's user avatar
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Gaussian approximation of Landau Ginzburg and Renoramalization Group

I am studing an introduction to the Renormalization Group (RG); during my course my prof. came up saying that: Landau-Ginzburg (LG) theory truncated at Gaussian order is exact at the critical point. ...
Federico De Matteis's user avatar
4 votes
0 answers
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Wilsonian effective action and dimensional regularization

In the Wilsonian approach to QFTs, QFTs are treated as effective field theories which are reliable at some UV cut-off $\Lambda_{eff}$, We then integrated out high energy modes and see how couplings ...
Arian's user avatar
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Landau Ginzburg path integral (PI) for the Ising model at gaussian order

I am stick with a problem in computing explicitely the gaussian PI in the Landau-Ginzburg theory for the Ising model. If we do a procedure of coarse graining, we can define $m(x)$ as a continuous ...
Federico De Matteis's user avatar
1 vote
1 answer
75 views

How to derive this equation about chiral lagrangian?

I'm learning chiral effective field theory from a paper. The NG boson field are collected in the matrix form as and the chiral fields U and u are defined by When there is no other field, the chiral ...
auntologist's user avatar
2 votes
0 answers
45 views

How does the expansion around the free theory relate to the idea of Gaussian fixed point in RG?

I have been wondering about the relationship between the Wilsonian picture of renormalisation, and the perturbative picture for quite some time now (in the context of QFT). What I am puzzled about ...
Werner Einstein's user avatar
2 votes
0 answers
53 views

Are there universality classes not found through a Ginzburg-Landau like free energy expansion

Usually the real free energy of a system is too complex to be exactly computed, thus one either expands it in power/gradient series or simply builds it from symmetry considerations. For example: $$F[\...
Syrocco's user avatar
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