All Questions
7
questions
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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
0
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2
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122
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Is there any physical reason behind the choice of Lie group in a Yang-Mills theory?
A Yang-Mills theory can be constructed for any Lie group that is compact and semisimple. The motivation behind this is discussed in this question. Is there any physical reason we choose $SU(3)$ or $U(...
- 3,350
2
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0
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68
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Abelian theories with more than one charge
I have a question about the non-abelian character of QCD. In order to write a gauge-invariant Lagrangian, there must be a term with the strength tensor $X^{\mu\nu}_{a}X_{\mu\nu}^{a}$ where
$$
X^a_{\mu\...
1
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2
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746
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How does the underlying symmetry of QCD imply the allowance of a 4-gluon vertex?
Quantum chromodynamics allows for a four-gluon vertex such as this, in a diagram
Such a vertex would never be allowed in quantum electrodynamics, which has an underlying U(1) gauge symmetry.
I know ...
- 324
2
votes
1
answer
529
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$U(N)$ & $SU(N)$ : What's the conceptual difference in Gauge Theory?
I know the mathematical difference that one means $ absolutevalue(det) = 1$ and one means det = 1 (rotation) and that ones the subgroup of the other and so on.
But:
has a local/gauged $SU(3)$ ...
- 91
4
votes
1
answer
2k
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Why quarks in the fundamental and gluons in the adjoint?
I have been told that in gauge theories
“fermionic matter goes in the fundamental rep of $SU(N)$, while gauge fields go in the adjoint rep”.
I understand how this works, and for instance, in QCD,...
- 1,154
2
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2
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696
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Reasons for choosing $SU(3)$ as the color group vs. $SO(4)$
What are the reasons that $SU(3)$ is used for QCD?
Why wouldn't the simpler & smaller group $SO(4)$ make a better candidate?
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