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.

Filter by
Sorted by
Tagged with
18
votes
2answers
2k views

What is the Wilsonian definition of renormalizability?

In chapter 23.6, Schwartz's quantum field theory book defines renormalizability as follows, paraphrasing a bit for brevity: Consider a given subset $S$ of the operators and its complement $\bar{S}$....
22
votes
1answer
3k views

Difference between 1PI effective action and Wilsonian effective action?

What is the simplest ay to describe the difference between these two concepts, that often go by the same name?
26
votes
5answers
5k views

Why should the Standard Model be renormalizable?

Effective theories like Little Higgs models or Nambu-Jona-Lasinio model are non-renormalizable and there is no problem with it, since an effective theory does not need to be renormalizable. These ...
5
votes
2answers
2k views

Finding the effective Hamiltonian in a certain subspace

In order to find the effective Hamiltonian in a subspace which is energetically well separated from the rest of the Hilbert space people try to find a unitary transformation which makes the ...
5
votes
1answer
184 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 ...
26
votes
3answers
3k views

A pedestrian explanation of Renormalization Groups - from QED to classical field theories

shortly after the invention of quantum electrodynamics, one discovered that the theory had some very bad properties. It took twenty years to discover that certain infinities could be overcome by a ...
15
votes
2answers
2k views

Is the effective Lagrangian the bare Lagrangian?

In standard (non-Wilsonian) renormalization we split the bare Lagrangian $\mathcal{L}_0$ into a physical Lagrangian $\mathcal{L}_p$ with measurable couplings and masses counterterms $\mathcal{L}_{...
10
votes
2answers
950 views

What is wrong with a nonrenormalizable theory?

Non-renormalizable theories, when regarded as an effective field theory below a cut-off $\Lambda$, is perfectly meaningful field theory. This is because non-renormalizable operators can be induced in ...
25
votes
7answers
2k 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 ...
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 $\...
11
votes
5answers
968 views

Could the full theory of quantum gravity just be a nonrenormalizable quantum field theory?

This may be more of a philosophical question than a physics question, but here goes. The standard line is that nonrenormalizable QFT's aren't predictive because you need to specify an infinite number ...
5
votes
2answers
503 views

Wilsonian picture of renormalization and $\phi^4-$theory

What is the criterion of renormalizability in the Wilsonian picture? In this picture, why is a theory with $\phi^4$ interactions renormalizable and a theory with $\phi^6$ interaction is non-...
8
votes
2answers
605 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?
4
votes
1answer
245 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 \...
4
votes
3answers
402 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 ...
19
votes
1answer
2k views

Why do irrelevant operators require infinitely many counterterms?

As far as I understand it, in the Wilsonian picture of renormalization, we view a theory as having some fixed cutoff and bare couplings, and integrate out high-momentum modes to understand what ...
7
votes
1answer
827 views

Renormalizing composite operators

Consider the QED Lagrangian, \begin{equation} {\cal L} = \bar{\psi} ^{(0)} ( i \partial_\mu \gamma^\mu - m ) \psi ^{(0)} - e A _\mu ^{(0)} \bar{\psi} ^{(0)} \gamma ^\mu \psi ^{(0)} - \frac{1}{4} ...
14
votes
1answer
425 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....
10
votes
1answer
835 views

Basic question about the S-Matrix, Unitarity and Effective Field Theory

Consider scattering some particles in a state collectively denoted by $i$ to a final state denote by $f$. The scattering amplitude, S-matrix is then defined by: $S_{fi}\equiv \langle f|e^{-iHt}|i\...
12
votes
1answer
1k 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 $\phi \rightarrow \phi_b + \phi$...
7
votes
2answers
143 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 $$\left\langle0|j^{\mu5a}(x)|\pi^b(q)\right\rangle=-if_\pi \delta^{ab} q^\mu e^{-iqx}$$ ...
3
votes
1answer
502 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 ...
7
votes
1answer
508 views

The non-renormalizable $\phi^6-$theory as an effective field theory

Let the non-renormalizable $\phi^6$ theory behaves as a low-energy, effective field theory, and works perfectly well below a finite energy (or momentum) scale $\Lambda$ for a system. In this theory, ...
5
votes
1answer
168 views

Renormalizing with external momenta set to zero

I've often seen in textbooks that authors renormalize diagrams by setting external momentum to zero. Under what conditions is this justified? An example of this is done in Manohar and Wise's book on ...
5
votes
1answer
123 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. ...
5
votes
0answers
712 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 $r\...
3
votes
1answer
183 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....
4
votes
1answer
185 views

Range Of An Interaction

Why is the Compton wavelength $\lambda_c=\frac{\hbar}{mc}$ used as a sensible measure for the range of an interaction, where $m$ is the mass of the corresponding mediator?
3
votes
1answer
211 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 $\Lambda\rightarrow\infty$...
2
votes
1answer
211 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
1answer
415 views

What does it mean by a nonrenormalizable operator being induced in a Lagrangian?

I have heard that nonrenormalizable operators (i.e., mass dimension greater than 4) can be "induced" in the Lagrangian (that we started with) via loop effects. However, I do not understand what does ...