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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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} ...
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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 ...
2
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1answer
937 views

Trace of Fermion Loops in Effective Field Theories

I'd like to know whether we need to take the trace of fermion loops in effective theory in the same way that we need to do so for renormalizable theories. At first thought, it seems obvious that ...
4
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1answer
1k views

Power counting with a cutoff

In Effective Field Theory video lectures found here, the professor explained power counting in effective field theories and the difficulties of power counting associated with loop diagrams. He then ...
2
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0answers
307 views

Effective Field Theories of QCD

Recently, I am studying the online course Effective Field Theory provided by MIT OCW. Prof. Stewart gives a nice picture to summarize the effective theories: As a newbie in this field (I only have a ...
4
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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?
1
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1answer
140 views

Nuclear forces and Chiral Effective field Theory

I am new to this field "nuclear forces and Chiral Effective field Theory". while reading this paper http://arxiv.org/abs/nucl-th/0006014 . I have got few question: How many different version of CD-...
10
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1answer
834 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\...
15
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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}_{...
8
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1answer
736 views

How to understand the Lagrangian of the standard model, effective or “fundamental”?

I have a question about understanding the Lagrangian of standard model, should we view it as a "fundamental" or effective theory? The "fundamental" theory here means the theory with physical cutoff (...
3
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2answers
769 views

Is the big desert hypothesis a wilder assumption than the see-saw mechanism to explain neutrino masses?

Sometimes I see comments about the big desert hypothesis that I don't understand. For instance in a famous blog : ...This is based on a renormalization group calculation extrapolating the Higgs ...
8
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1answer
868 views

What does it mean to renormalize an effective field theory?

This is in reference to slide 19 of this talk "As always in Effective Field Theory, the theory becomes predictive when there are more observables than parameters" Can one explain what this exactly ...
19
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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 ...
11
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1answer
529 views

Chiral perturbation theory: what is the Quark Condensate? why expand in $U$ rather than Goldstone fields?

I'm studying Chiral Perturbation Theory ($\chi PT$) from Scherer's Introduction to Chiral Perturbation Theory. What I am currently having some trouble understanding are two things: The quark ...
8
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0answers
379 views

Finite quantum gravity?

I'm working through an article that has some questionable assertions. The article is by Frank Tipler, "The structure of the world from pure numbers". (I'm going to ignore the fact that some of Tipler'...
22
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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?
15
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1answer
326 views

6d Massive Gravity

Massive gravity (with a Fierz-Pauli mass) in 4 dimensions is very well-studied, involving exotic phenomena like the van Dam-Veltman-Zakharov (vDVZ) discontinuity and the Vainshtein effect that all ...
14
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3answers
2k views

Feynman diagrams in effective theories

I've been seeing many feynman diagrams lately that I can't quite interpret yet. I've heard a basic Quantum Field Theory lecture and so to me, a Feynman diagram is simply a mnemonic picture to quickly ...
26
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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 ...
26
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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 ...
11
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2answers
1k views

Steps for going from Polyakov action to low-energy effective action (SUGRA?) in String Theory

A lot of string-theory questions have been asked here. This one is, hopefully, different in that this inquiry is specific and the expected answer would be more mathematical than philosophical in ...