All Questions
16
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A list of failed attempts towards a proof of confinement [closed]
Can one give a list of failed or open attempts (not necessarily Supersymmetric) towards a proof of confinement in 4d regarding YM or QCD?
- 1,268
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0
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Wilson loop is not an element of $\mathrm{SU}(3)$ in color deconfinement
The center symmetry in QCD comes from the
$$a\ \mathcal{P}\mathrm{exp}\left(ig_s \int_C dx^\mu \ A_\mu(x)\right) a^{-1} = \mathcal{P}\mathrm{exp}\left(ig_s \int_C dx^\mu \ A_\mu(x)\right),$$
where $C$ ...
- 87
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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
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
2
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783
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QCD energy scale $\Lambda_{\rm MS} $, $\Lambda_{\rm QCD}$, ...?
Why there seems to be different conventions of QCD energy scales? Is that due to the running coupling?
For example in Wikipedia https://en.wikipedia.org/wiki/Coupling_constant#QCD_scale:
$$
\Lambda_{\...
- 4,336
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
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696
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Why is color confinement a difficult problem?
Assuming color force follows a constant rule of force instead of an inverse square rule of force. And that red, green and blue are all attracted to each other.
Why is color confinement considered a ...
user84158
4
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answers
143
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What is the relation between the Gribov problem and color confinement?
I have heard that the Gribov problem is in some way related to color confinement (For instance: Gribov copies and confinement). Although I understand what both the Gribov and confinement problems are, ...
- 17.8k
19
votes
1
answer
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Inverse square rule for strong forces
Most of the forces induced by a point particle follows the $1/r^2$ rule. Then why does the strong force not obey it?
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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
1
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Could we draw field lines for colour charge?
Electromagnetic charge can be represented with field lines. These are pleasingly intuitive and can be used to visualise Gauss's Law and Maxwell's Laws. Later on Gauss and Maxwell get rolled into a ...
- 183
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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
5
votes
2
answers
927
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Yang-Mills theories, confinement and chiral symmetry breaking
I was thinking about hadrons in general Yang-Mills theories and I have some doubts that I'd like to discuss with you.
Suppose that we have a Yang-Mills theory that, like QCD, tend to bind quarks ...
- 300
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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
35
votes
2
answers
5k
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What does it mean that there is no mathematical proof for confinement?
I see this all the time* that there still doesn't exist a mathematical proof for confinement. What does this really mean and how would a sketch of a proof look like?
What I mean by that second ...
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