All Questions
12
questions
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Asymptotic Freedom QCD
I'm trying to understand the derivation of asymptotic freedom with the renormalisation group equations. I'm reading Taizo Muta's book on QCD. What I don't understand is how he obtains the last ...
- 15
0
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1
answer
81
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Possible cases of matter fields for $SU(2)$ theory which retains asymptotic freedom?
Let us assume $4$ spacetime dimensions.
QCD, the $SU(3)$ gauge theory with quarks as the matter fields, have the asymptotic freedom property as long as there are 16 quark flavors of mass below the ...
- 1,669
0
votes
0
answers
244
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One-loop renormalization of the gauge coupling
Quoting Yuji Tachikawa, chapter 3 of "${\cal N}=2$ Supersymmetric Dynamics for Pedestrians":
Recall the one-loop renormalization of the gauge coupling in a general Lagrangian field theory $$...
user242231
3
votes
1
answer
258
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What makes the (non-abelian) strong interaction so special that it leads to confinement?
The strong interaction has a coupling constant of $\alpha_s(91GeV)\approx 0.1$ whereas the weak interaction has a much lower coupling constant $\alpha_w \approx 10^{-6}$. Both theories are non-abelian ...
- 9,778
3
votes
0
answers
124
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The 1-loop anomalous dimension of massless quark field for $SU(N)$ gauge theory with $n_f$ quark flavours
Considering $SU(N)$ gauge theory with $n_f$ massless quarks
I want to find the anomalous dimension to order of 1-loop of the massless quark field, that defined by: $$\gamma_q(g^{(R)})=\frac{1}{2Z_q}\...
5
votes
1
answer
375
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How can we tell a theory is confining?
Physically, I understand what it means for a theory to be confining. The elementary particles are not observable, but only composite particles are. The classic example is QCD, where quarks are ...
- 3,514
0
votes
0
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288
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Intuition for Asymptotic Freedom
In QED, the $\beta$-function has a positive sign. This means that the coupling increases at higher energies, or equivalently, smaller length scales. This picture is made intuitively clear by the ...
user240990
5
votes
2
answers
530
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What is relevant for Yang-Mills theory below $d = 4$?
There are two ways to write the Lagrangian for Yang-Mills, differing by the scaling of the Yang-Mills field. Fancy theorists tend to write
$$S = \int d^dx \, \frac{1}{4e^2} \, \text{tr}(F^2)$$
while ...
- 103k
7
votes
1
answer
442
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Is Yang-Mills theory confining in any dimensions?
What is the current understanding of Yang-Mills theory (pure non-Abelian gauge theory without matter field) in the infrared limit? (To avoid the subtlety of renormalizability, we may restrict our ...
- 11.9k
5
votes
1
answer
262
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Would the existence of more than 16 quark flavors make QCD deconfinning?
Consider the QCD beta function. Its expansion in powers of the coupling is
$$\beta(\mu)=-(\beta_0a(\mu)+\beta_1a^2(\mu)+\ldots)$$
where $a=\alpha/4\pi$. For simplicity let's neglect everything but ...
- 6,067
4
votes
0
answers
322
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Why is QCD hard to solve if I know the beta functions?
Why is it still hard to solve QCD if we know the beta functions of the coupling? Aren't only the loops causing problems? And am I not able to write every possible interaction exact at tree-level with ...
- 2,147
16
votes
1
answer
2k
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Are "confinement" and "asymptotic freedom" two sides of the same coin?
On Wikipedia it says that the two peculiar properties of quantum chromodynamics (QCD) are: confinement and asymptotic freedom.
Asymptotic freedom is the idea that at low energies we cannot use ...
- 5,228