Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

0
votes
0answers
16 views

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 ...
1
vote
1answer
45 views

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 ...
3
votes
1answer
91 views

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 ...
1
vote
0answers
35 views

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 ...
0
votes
0answers
29 views

Piecewise solution to Euler-Lagrange equations

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 ...
4
votes
1answer
174 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 \...
1
vote
1answer
57 views

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. ...
6
votes
1answer
84 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 ...
1
vote
0answers
39 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 ...
2
votes
2answers
53 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, ...
3
votes
0answers
41 views

Effective field theories from QCD

Is there a way - at least formally - to derive theories like chiral perturbation theory or heavy baryon effective theory from QCD? As an example: is it possible first to introduce the effective ...
2
votes
1answer
77 views

Why does the Lagrangian Density have to be a polynomial of the field?

In a lecture, a professor appeared to have said that the Lagrangian can only contain terms that have powers of $\phi$ and a term with $\partial_\mu \partial^\mu \phi$ . I imagine this would make any ...
2
votes
1answer
119 views

${\cal N} = 1$ SUSY Non-renormalization theorem

In Ref. 1, on Page 53, the ${\cal N} = 1$ SUSY non-renormalization theorem is derived. One first specifies the symmetries of the general ${\cal N} = 1$ SUSY action in the superspace formalism, and ...
2
votes
0answers
70 views

Why is the standard model renormalizable if we believe it is an effective theory? [duplicate]

We believe that the standard model is only an effective field theory of its true UV completion. However, effective theories have dimensionful couplings and are not renormalizable. The standard model ...
0
votes
0answers
36 views

High-energy effective field theory

Usually when one speaks of effective field theories, one is looking to integrate out certain fields which are typically heavy in comparison to the regime of interest. That is one has a theory at a ...
1
vote
1answer
123 views

How to fuse quantum mechanics and general relativity?

I am very new to this topic but I have started reading Kevin Wray's lecture notes about string theory (PDF) and in the introduction he says: "Sometimes it is said that we don’t understand how to ...
1
vote
0answers
45 views

Computing the Wilsonian Action

Equation 12.5 of Peskin&Schroeder reads $$Z = \int\left[\mathcal{D}{\phi}\right] e ^{-\int d^dx \, \frac{1}{2} (\partial \phi)^2 + \frac{m^2}{2}\phi^2 + \frac{\lambda}{4!}\phi^4} \cdot \...
1
vote
0answers
52 views

Why is vanishing beta function associated with scale-invariance?

Why is vanishing beta function associated with scale-invariance? Coupling constants have change rate of zero at some scale, but how is that related to scale-invariance? Association of vanishing beta ...
1
vote
0answers
43 views

Symmetries of effective field theory of hydrodynamics: a confusing calculation

This is a very specific question about a paper by P. Glorioso and H. Liu that can be found here https://arxiv.org/pdf/1805.09331.pdf. In particular I want to understand how the authors get from the ...
1
vote
1answer
63 views

Is there any threat to the results of our effective field theories from unknown higher energy theories?

We use renormalization arguments (and experiments) to change the couplings of a theory and suppress the higher energy physics (saying things like “whatever the fundamental theory, this will be true of ...
0
votes
1answer
63 views

Can a unified physics theory have a smaller number of couplings than its effective field theory?

Suppose that we have a QFT that has $n$ number of physical coupling constants, or there are $n$ coupling constants required to perturbatively renormalize the given QFT. Suppose this QFT to be an ...
6
votes
1answer
145 views

Recovering nonrelativistic quantum mechanics from quantum field theory

In quantum field theory -- specially when applied to high energy physics -- we see that the requirements of Lorentz invariance, gauge invariance, and renormalizability strongly limit the kinds of ...
1
vote
0answers
53 views

QED vertex correction, proper vertex function and meaning

I might be making great confusion in trying to interpret proper vertex function. I'm studying QED vertex correction. I'm just going to write down the pieces of the puzzle. So I know that the ...
4
votes
0answers
119 views

What's the “effective potential” for photons in $X$-ray diffraction?

The slickest way to introduce $X$-ray diffraction is to invoke scattering theory in quantum mechanics. One treats the incoming photon as just another particle in a scattering problem; by Fermi's ...
4
votes
2answers
275 views

Comparing momentum cutoff and lattice regularization in Quantum Field Theory

Usually, it is heuristic to say that we can understand a QFT with a momentum cutoff $|k|<\Lambda$ by imagining that the system is living on a lattice. I would like to ask: (1) Is there any ...
3
votes
1answer
145 views

What does soft symmetry breaking physically mean?

A symmetry can be explicitly broken by adding terms in the Lagrangian that aren't compatible with the symmetry, and we say the symmetry is softly broken if all these terms have positive mass dimension....
3
votes
1answer
65 views

Invariant terms of Chiral Lagrangian

Stupid question. Consider a global SU(N) theory spontaneously broken. I want to write the EFT of the Goldstone bosons in terms of the field $$ \Pi = e^{i\pi^a T^a} $$ where $T^a$ are the SU(N) ...
3
votes
1answer
176 views

Feynman rule of $\bar{\phi} \phi F_{\mu \nu}F^{\mu \nu}$ and its corresponding 4-photon scattering amplitude

Consider the Lagrangian: $$\mathcal{L}~=~-\frac{1}{2}\bar{\phi} \square \phi - \frac{1}{4}F_{\mu \nu}F^{\mu \nu} + \lambda \bar{\phi} \phi F_{\mu \nu}F^{\mu \nu}$$$\hspace{200px}$ The vertex Feynman ...
0
votes
0answers
42 views

Lorentz invariance hereditity from fundamental to phenomenogical models

I'm taking the courage to ask here a question that could be proven naive- if so, it should be closed and I will delete it. If we assume a QFT with Lorentz invariance, is there a way to show, besides ...
2
votes
1answer
78 views

Wilsonian RG approach to Fermi liquid theory

In modern terms, Landau's theory of Fermi liquids is understood as the fixed point of a Wilsonian RG as one scales towards the Fermi surface. Shankar and others use the RG interpretation to explain ...
14
votes
1answer
386 views

Why do we care about old-style, counterterm renormalizability?

There are a few different definitions of renormalizability that are standard in quantum field theory textbooks. They're all called the same thing, but I'll make up names to make the distinctions clear....
4
votes
3answers
325 views

Can dimensional regularization be viewed as a soft version of a Wilsonian cutoff?

In the Wilsonian picture of renormalization, a quantum field theory is defined to have degrees of freedom only up to an energy scale $\Lambda$. The results of low-energy experiments shouldn't change ...
1
vote
0answers
37 views

The 3 graviton species

Recently, there is some speculation about the fact that quantum gravity could imply the existence (naturally, even without extra dimensions or any other stuff) of 3 gravitons: a massive spin-2 ghost ...
2
votes
1answer
155 views

Diagram versus gradient expansion

Suppose one starts from the Dyson equation $\int dy\left[G^{-1}\left(x_{1},y\right)\cdot G\left(y,x_{2}\right)\right]=\delta\left(x_{1}-x_{2}\right)$ with $G$ some Green's function. One may usually ...
1
vote
1answer
248 views

How does 11D Supergravity relate to M-Theory?

I know Type IIA/B, Type I, HO, & HE are related through the T and S Dualities. However, how does SUGRA factor in here? What exactly is 11D SUGRA’s significance in M-Theory? Some seem to suggest ...
2
votes
0answers
31 views

What is the meaning of the Wilson coefficients $C_{S,P,T}$ in the electron-nucleon interaction?

I am doing a project on electric dipole moments in supersymmetry. My background is in high energy physics, so I am having trouble fully grasping the nuclear interactions. Part of that includes ...
1
vote
0answers
44 views

pNRQCD at high pT

pNRQCD is an effective field theory for heavy Quarkonium, where the velocities are non-relativistic due to large mass. But is pQCD applicable when the Quarkonium is moving at high velocities? The ...
2
votes
1answer
52 views

Renormalising $\Delta$ baryon mass in chiral effective field theory

I have essentially no experience of quantum field theory, other than a superficial knowledge of some basic ideas - my apologies if I've phrased anything unusually or made any mistakes in my question ...
2
votes
1answer
242 views

What's the running coupling of gravity?

Pictures like the one below are often used to talk about grand unification. I've never heard any physics textbook really talk about the running of the gravitational coupling constant $G$, but some ...
6
votes
1answer
282 views

What diagrams to include in Wilson's Approach?

In the Wilson's approach to renormalization we split the field into two parts; a high momentum part and a low momentum part. We then integrate out the high momentum terms. Consider the case of $\phi^3$...
2
votes
2answers
200 views

Do we “get rid of” irrelevant operators in as we consider low-energy effective theory?

On reading the section 12.1 of Peskin and Schroeder's (P&S) QFT on "Wilson's Approach to Renormalization Theory", I gathered the impression that in the Wilsonian approach, one starts by analyzing ...
1
vote
0answers
85 views

Difference between average effective action and Wilsonian effective action?

There is a good description about " Difference between 1PI effective action and Wilsonian effective action? " here. Now, what is the difference between average effective action, which we use that in ...
25
votes
7answers
1k views

Dirac once said that renormalization is just a stop gap procedure, and there had to occur a fundamental change in our ideas. Did something change?

Once upon a time, Dirac said the following about renormalization in Quantum Field Theory (look here, for example): Renormalization is just a stop-gap procedure. There must be some fundamental ...
3
votes
2answers
179 views

Does every regularization/renormalization approach gives running coupling constants?

I'm studying different tools for regularization and renormalization. Until now I vaguely understand 1) the wilson approach to renormalization where one thinks of the theory as essencially effective ...
5
votes
3answers
329 views

Srednicki QFT Chapter 29: Feynman diagrams for calculating the effective action

I am trying to work my way through Srednicki Chapter 29 on Wilson's approach to renormalisation. However I am unsure why the Feynman diagrams Srednicki considers and calculates in this chapter are the ...
18
votes
1answer
948 views

What's the relation between Wilson Renormalization Group (RG) in Statistical Mechanics and QFT RG?

What's the relation between Wilson Renormalization Group(RG) in Statistical Mechanics and QFT RG? For easier to compare, I choose scalar $\phi^4$ in both cases. Wilson RG: Given $\phi^4$ model, $$Z=...
4
votes
3answers
281 views

Can the Lagrangian of an effective field theory have higher derivative terms?

For example, the effective field theory Lagrangian with cutoff $\Lambda$ for the renormalizable $\varphi^4$ theory is $$\mathcal L_{\mathrm{eff}}(\varphi;\Lambda)=\frac{1}{2}Z(\Lambda)\partial_\mu\...
3
votes
1answer
160 views

What does the cut-off $\Lambda$ stand for in the theory of QED?

The bare electron mass $m_0$, in QED, changes as $$m_0\to m=m_0+\delta m\Big(\frac{\Lambda}{E}\Big)$$ where high momentum modes from $E$ to $\Lambda$ has been integrated out. What scale does the cut-...
22
votes
3answers
3k views

Does QED really break down at the Landau pole?

In QED, the fine structure constant $\alpha$ runs upwards in the UV, with a loop calculation (involving a geometric series of the vacuum polarisation diagram) indicating a divergence in $\alpha$ at $\...
1
vote
0answers
22 views

Is it good approximation to use the Fermi theory in terms of proton and neutron for the given processes?

Suppose the processes $$ p+\gamma \to n + \bar{l} + \nu_{l}, \quad p+\gamma \to p+\bar{\nu}_{l} + \nu_{l}, $$ where $p$ denotes a proton, $\gamma$ - a photon, $l$, $\nu_{l}$ - a lepton and ...