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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Kinetic mixing, and a bare mass?
I've been reading the following classic paper by Bob Holdom "Two U(1)s and $\epsilon$ charge shifts", and I'm attepting to derive the expression for $\chi$. In particular, I am computing the ...
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Linearization of $\beta$-functions around Gaussian fixed points
I was reading section 8.4.4 of the book "Condensed Matter Field Theory" by Altland & Simons and I ended up with a very specific question that I couldn't resolve.
After finding the ...
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Spontaneous emission as dissipation and fluctuation
Suppose we have some sort of medium and we want to build an effective theory of light inside. Of course we want to calculation the dielectric constant, which in turn is determined by the ...
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Standard model and gravity gauge theory
I will briefly explain my understanding on the subject.
In the following explanation i refer to the Poincarè group meaning the group:
$$\mathcal{P}_{1,3} = \mathbb{R}^{1,3} \rtimes Spin^+(1,3)$$
The ...
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What can an EFT tell one about the ''underlying'' theory?
I was reading about effective field theories and wondering how much an EFT can tell you about the ''underlying'' theory which is then reflected in the EFT. Can one extrapolate back from what one sees ...
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A question on Schwartz's derivation of the Euler-Heisenberg Lagrangian
In Subsection 33.2.2. of Schwartz's Quantum Field Theory and the Standard Model, he starts to derive the Euler-Heisenberg effective Lagrangian by "replacing" the field which is being ...
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Conformal manifold of a supersymmetric field theory
I'm trying to understand what exactly is the conformal manifold of a theory. If I understand it right, the conformal manifold is the space of couplings.
From that point of view, it is just a subset ...
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Justification for the derivative expansion in the Exact Renormalization Group
In the Exact Renormalization Group formalism, specifically the formalism of Wetterich, one writes down an evolution equation for the effective average action $\Gamma_k[\varphi]$, see f.ex
$$
\...
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Kinetic Terms for Interacting Massive Vector Field
The kinetic term in the standard Lagrangian for a vector field, whether massive or not, is
$$-\frac{1}{4}F^{\alpha\beta}F_{\alpha\beta}=-\frac{1}{2}(\partial_\alpha V_\beta \partial^\alpha V^\beta - \...
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When to consider and when not to consider the loop contributions from light quarks?
Consider the following Lagrangian:
$$
\tag 1 \mathcal{L} = \frac{\partial_{\mu}a(x)}{f}\sum_{q}\bar{q}\gamma^{\mu}\gamma_{5}q
$$
This is a Lagrangian of the axion-like particles (ALPs) $a$ interacting ...
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Effective field theory of massive spin-1 and spin-2
I'd like to understand what could be the use of an effective field theory (EFT) of a single massive particle of spin 1 or 2, or simple modification of these (see below). By EFT, I mean the most ...
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Thirring Model effective potential
I have the lagrangian for the Thirring model coupled with vector interaction $V^\mu$ in the large-$N$ approximation:
\begin{equation}
\mathscr{L}=\bar{\psi}\left(i \gamma^\mu\partial_\mu-m - \gamma_\...
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Do irrelevant directions contribute to the IR dynamics?
Is it not a misnomer to call in a non-perturbative setting an irrelevant direction irrelevant?
I know that it comes from perturbation theory where an irrelevant direction is irrelevant for the IR ...
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Beta function of $\phi^4$ from RG equation
I am currently following David Tongs lecture notes on statistical field theory (Link to the script) and I have an issue with the calculation of the beta-function from the RG equations (equation (3.45))...
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Indices of $(\text{Riem})^3$?
This question relates to writing higher curvature terms in momentum space with respect to GR as an effective field theory.
I know that $R_{\alpha\beta\mu\nu} \sim \partial_\beta\partial_\mu h_{\alpha\...
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How does the renormalization process differ between actions with and without diffeomorphism invariance?
If I have an action that is not invariant under a change of coordinates. Does this effect the renormalizability of the theory?
The procedure of renormalizing a field theory essentially boils down to ...
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Simple examples of compactification [closed]
I am starting out on some research and I am trying to find basic examples of compactification to start off with, and then I want to work my way up to more complicated items such as having an action ...
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Renormalization of Two Scalar Field Theory at Tree-Level and One-Loop Levels
I have been given a problem on renormalization, but due to my inexperience, I don't understand what to do with it. Here is the statement:
Consider a theory of two real scalar fields $\phi$ and $\Phi$ ...
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Is a QFT always an EFT coming from something deeper?
(I have already read this post but my question is different)
Reading Ch. 12 of Weinberg's Quantum Field Theory Vol. 1, he states that all realistic (interacting) QFTs are now believed to be EFT of ...
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Degree of divergence of subdiagram
The proof of the Appelquist-Carazzone theorem involves analyzing the behaviour of an internal subdiagram which is a fermion loop with $F$ incoming vector lines. The mass of the fermion is assumed much ...
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Looking for examples of Polchinski's ERG
This question is related to my older question on the Exact Renormalization Group.
I've read through the first half the Rosten review (https://arxiv.org/abs/1003.1366) and the Bervillier paper (https://...
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Are large logarithms tied to dimensional regularization?
When introducing the renormalization group many textbooks start by stating that scattering amplitudes often contain logarithms of the form $\log\frac{\mu^2}{p^2}$, where $p^2$ is the characteristic ...
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Calculation of a RG-transformed energy functional
Consider the Landau-Wilson energy functional in a constant magnetic field:
$$E[m] = \int d^dx \left[\frac{1}{2} \vec\partial m(x))^2+ \frac{1}{2} r_0 m^2(x) + u_0m^4(x) + hm(x)\right]$$
We will ...
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Conceptual dobuts about EFTs and the decoupling of heavy fields
I've tried to synthetize some of my misconceptions in the following statements. I just like to know which of them are true and get some intution about them.
EFTs exist only if heavy fields decouple (...
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Exact Renormalization Group
I'm studying the Exact Renormalization Group in QFT.
I've found some pretty OK references already (see https://arxiv.org/abs/hep-th/0002034 and https://arxiv.org/abs/1003.1366), but I was wondering if ...
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Observables and RG flow
I am confused about a standard thing regarding renormalization group eqn. The primary motivation of writing the RG eqns are observables do not depend on the UV cutoff $\Lambda$ (Wilsonian) or ...
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Wilsonian RG vs. continuum RG
As far as I understand one classifies the renormalization group (RG) into the Wilsonian RG and the continuum RG. The Wilsonian RG gives finite predictions by introducing a cutoff $\Lambda$ and absorbs ...
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Studying the Renormalizability of classically equivalent theories
I am currently studying the effect that a massive, uncharged, non-minimally coupled spin $\frac{1}{2}$ field has on the background geometry upon quantization, and compare this with results in General ...
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Wilsonian renormalisation / Polchinski renormalisation equation. Why is the factor in the kinetic term infinite for large momenta?
For Polchinski renormalisation equation, a smooth cutoff is introduced that is essentially a factor of $ 1 $ up until the cutoff region in the kinetic term. Beyond this "cutting-off" region (...
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Asymptotic freedom of the $\phi^4$ theory depending on spacetime dimensions?
I heard that $\phi^4$ theory in $4-$dimensions is NOT asymptotically free.
But in lower dimensions like $2$ and $3$, it is said to be asymptotically free.
However, what confuses me is that in $3-$...
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Derivative of a "particle" field
Working with Lagrangian we often encounter derivatives of particles fields, for example let's consider the first term of the LO chiral Lagrangian
$$ \mathcal{L}_{B\phi}^{LO}=\text{Tr}[\overline{B}(i\...
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EFT operators to Feynman Diagrams
I have this paper arXiv:1410.4193 which contains a complete list of pre-EWSB dimension-7 EFT operators, and I have taken them and 'converted' them to post-EWSB operators. As an example, from the $\psi^...
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Asymptotic Freedom and the Continuum Limit
Suppose I have a family of effective field theories, parametrized by a cut-off $\Lambda$ and a coupling constant $g$ and specified in terms of generating functionals $Z_{\Lambda,g}(J)$. Asymptotic ...
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Wilsonian effective field theories and renormalization due to marginal and irrelevant operators
In the top-down approach, e.g., Fermi interaction obtained from EW Lagrangian, the loop corrections (using dimensional regularization) and renormalization of $G_F$ are done using the full EW ...
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How to read renormalization group flow plots?
From what I know, the renormalization group tells us how the coupling constants of a theory change as the energy scale is varied. Thus as you vary the energy scale you trace out a path or flow in the ...
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Trouble understanding Wilsonian renormalization
I have been attempting to go through Chapter 12 of Peskin & Schroeder, but I have been having a very tough time. In particular I have been having trouble following this chapter much beyond page ...
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Uniqueness of high temperature RG fixed point
Given a $\phi^4$ theory in $d<4$
$$S_{\Lambda} = \int d^dx \left[\frac{1}{2}(\partial_i \phi)^2 + \frac{1}{2} \mu_0^2 \phi^2 + \Lambda^{d-4} \tilde{g}_0 \phi^4 \right]\,,$$
the corresponding RG ...
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Consistency of One-Pion Exchange with Selection Rules for NN Pion Production (in Chiral EFT, e.g.)
Hope you're ready for a long question, but I think quite an interesting one!
One-pion exchange is an established nucleon-nucleon potential which is well-defined for any joint angular momentum state of ...
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How to compute the susceptibility of the Polyakov loop in Monte Carlo lattice field theory?
I am having troubles understanding the definition of the susceptibility of the Polyakov loop give, for example, in the book by Gattringer, Lang "Quantum Chromodynamics on the Lattice", page ...
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Are all QFTs, EFTs?
Is every Quantum Field theory, including CFTs, an Effective Field Theory?
Can every interacting CFT become the infra-red fixed point of some high energy QFT?
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Integrating high momentum modes using Wilson's approach to renormalization
In Section 12.1 of Peskin & Schroeder, they introduce the renormalization group for $\phi^4$ theory.
Let $b < 1$ and $\Lambda$ some UV cutoff. Define
$$\hat{\phi} = \begin{cases}
\phi(k) , \...
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Wilson Coefficients in the Standard Model
I'm not particularly knowledgeable in this area of physics. From my understanding as an undergraduate, Wilson coefficients are sets of parameters that arise from an effective field theory which ...
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Why rescale the kinetic term in Wilsonian renormalization?
I have been doing some reading on Wilsonian renormalization and also Effective Field Theories.
It's my understanding, and I could be wrong, that part of the process is to continually rescale the ...
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Do unresummed self-energy functions spoil RGE resummation?
I am aware, that the solution of the $\beta$-function contains a resummation of all large logarithms, but I fail to understand how this is actually relevant: The coupling constant is not an observable ...
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Understanding this abstract Lagrangian of effective field theory
I'm learning Wilson's approach to renormalization and the Effective Field Theory. Typically, the theory is defined by a Lagrangian valid up to some scale $Λ$. I saw these two definitions for 4-...
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Renormalization of quark bilinears
I'm looking at the one-loop corrections to the amputated quark two-point functions ($\Gamma_i$) with insertions of quark bilinears (indexed by $i\in\{S,P,V,A,T\}$) with off-shell legs in Euclidean QCD....
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What theory are we actually working in when "using" QED?
My understanding of QED is roughly that (please correct me if I have made a mistake, I am not very experienced in QFT):
Firstly, QED is not exact. At a certain energy scale, we have electroweak ...
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Is $\phi^5$ a descendant in $\phi^4$-theory (at the conformal Wilson-Fisher fixed point)?
I'm wondering if $\phi^5$ is a descendant in $\phi^4$-theory in $d = 4 - \epsilon$ at the conformal Wilson-Fisher fixed point, where the coupling constant is $\lambda$. The e.o.m. tells us that $\phi^...
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Effective Theory for Matter Fields Coupled to a Chern-Simons Field
Assuming that matter fields coupled with the background Chern-Simons field (or Maxwell-Chern-Simons field), I want to obtain the effective theory in terms of matter fields only, by integrating out a ...
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$\rm Tr[log( )]$ calculation to go from BCS to Ginzburg-Landau
It seems like calculating the effective action $|\Delta|^2 + Tr[ln(G^{-1})]$ give the Ginzburg Landau action.
\begin{equation}
G^{-1} =\begin{pmatrix} i\partial_t - H & \Delta \\
\Delta^* & i\...
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