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113 views

Computing things in Effective field theory

I find it hard to go through most of the homework problems in an effective field theory course. In fact I think I have developed a general disdain in solving hard Quantum field theory related ...
3
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0answers
64 views

Understanding the effective low-energy Lagrangian for hadrons

My course in Higgs Physics is discussing a two-nucleon low-energy effective theory of hadron interaction. With $\psi=(p,n)$, the pion is defined as $\vec{\pi}= i \bar{\psi}\vec{\tau} \gamma_5 ...
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0answers
60 views

Hamiltonian Operator for nonrenormalizable Effective Field Theories?

Assuming we have a Effective Field Theory, for example a Real Scalar Field Theory, defined through a Lagrangian density of the form $\mathcal{L}_{eff} = \frac{1}{2}\partial_\mu\phi \partial^\mu\phi - ...
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0answers
121 views

Effective Field Theory (EFT) decoupling top

The decoupling theorem of Appelquist-Carazzone says that if you want to decouple a particle, the low energy resulting theory need to be renormalizable. You can't do that for the top, because you break ...
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1answer
50 views

Effective field theory for fermion gas

Reading about fermion gas in a paper they used the following Lagrangian, which describes an effective field theory for nonrelativistic fermions (I neglect the four point interaction term). $$ L = ...
7
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2answers
176 views

Naive questions on the concept of effective Lagrangian and equations of motion?

Let us consider a LC circuit containing an electric dipole moment, the quantum system (electric field $E$ coupled with a dipole moment) can be described by the path integral $$Z=\int DEDxe^{i\int ...
7
votes
1answer
194 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 + ...
8
votes
1answer
93 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?
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0answers
64 views

What is a superfluid in field theoretic terms?

I'm wondering how one precisely defines a superfluid in terms of the effective field theory description. In Nicolis's paper http://arxiv.org/abs/1108.2513 there seems to be an extremely simple ...
3
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1answer
125 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 ...
4
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1answer
85 views

Quantum field theory defines its own bounds of applicability

I recall hearing in a lecture something along the following lines: "Due to some intrinsic feature of quantum field theory in general (or maybe it was the standard model?), we know where it is ...
3
votes
2answers
112 views

What is the logic of not regarding perturbative renormalizability as a fundamental requirement?

I read a statement in Becker and Becker's String Theory and M-Theory page 2. After pointing out the non-renormalizablity of GR by the dimension of gravitational constant, it is said: Some ...
2
votes
1answer
119 views

NRQCD: Why are quarks and anti-quarks treated independently?

I am studying these lectures on effective field theories and I am having some problems to understand how the Non-Relativistic QCD (NRQCD) Lagrangian is constructed. This theory is often used to ...
2
votes
1answer
46 views

Transformations of a left-handed gauge field

In a set of lectures I'm watching on Effective Field Theory the professor introduces a spurion vector field, $\ell_\mu$. He then says that we take it to transform as a "left handed gauge field" and ...
1
vote
1answer
173 views

Why does a spurion analysis work independently of the UV physics?

In short, my question is why does a spurion analysis work to produce the correct symmetry breaking terms regardless of the high energy physics? The context that this question arose is from an ...
3
votes
1answer
154 views

Effective theories and dimension six operators

What is the importance of dimension six operators in the study of physics beyond the Standard Model? Are these operators more relevant than dimension five operators like $HHFF$ or operators with ...
3
votes
2answers
144 views

What are threshold corrections?

As the title goes, what are threshold corrections in quantum field theory? In particular, I would be glad if a good reference is provided. Standard QFT books such as Peskin, Weinberg, etc seem to ...
2
votes
0answers
55 views

Energy interpretation of 1PI effective potential in Weinberg 16.3: is adiabatic turning on the current necessary?

In section 16.3 of Weinberg, he interprets the 1PI effective potential as the minimum of expectation value of the energy density under some constraint. The essential argument is \begin{equation} ...
6
votes
1answer
121 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} ...
3
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1answer
41 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
votes
1answer
121 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
votes
1answer
291 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 ...
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vote
0answers
78 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 ...
3
votes
1answer
50 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
vote
1answer
47 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 ...
7
votes
1answer
248 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 ...
1
vote
2answers
365 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 ...
5
votes
1answer
307 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 ...
9
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1answer
225 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 ...
6
votes
0answers
207 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 ...