All Questions
Tagged with quantum-chromodynamics group-theory
62
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
1
vote
1
answer
55
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How can I calculate action of $\mathfrak{su}(3)$ or other simple algebra ladder operators on "states" from the algebra commutators?
I wanted a way to "derive" Gell-Mann matrices for $\mathfrak{su}(3)$ and generalise this to other semi-simple algebras $\mathfrak{g}$. The way I wanted to approach this is start from the ...
- 785
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2
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121
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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
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74
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Difference between $ SU(3)$ and $ SU(3)_c $ group
I am reading quark model. I don't understand what's the meaning of a color $SU(3)$ or $SU(3)_c$ group and how it differs from a general $SU(3)$ group. Please elaborate.
- 377
2
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1
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433
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Why, in QCD, are quarks in the fundamental representation of $SU(3)$?
QCD is built from the notion that Dirac's Lagrangian should be invariant under gauge colour transformations.
Here, quarks are elements of $\psi_{\alpha,f,c}(x)$, where $\alpha$, $f$ and $c$ stand for ...
- 343
1
vote
1
answer
185
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Quantum Chromodynamics and Group Theory
I know nothing of QCD, but I was watching this youtube video and pondered on whether the additive structure described is a group, and if so, which is it?
As of now, I know the group must contain the ...
- 379
1
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1
answer
77
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Justifying the identification of eight gluons with the ${\bf 8}$ from ${\bf 3}\otimes{\bf 3}^*$
When we combine the fundamental ${\bf 3}$ and antifundamental ${\bf 3}^*$ of color $SU(3)$ of QCD i.e. single quark of three colors and a single antiquark of 3 anticolors, nine states are obtained. ...
- 11.8k
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82
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Why does full QCD not invariant under the $Z(3)$ symmetry group?
Hello and thank for the time you will take reading my question.
The $Z(3)$ symmetry can be defined as a simple global phase transformation: $$Z(3)=\left\{1, e^{\frac{i2 \pi}{3}}, e^{\frac{-i2 \pi}{3}}\...
- 43
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1
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236
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$\mathrm{SU(3)}$ structure constant values
The $\mathrm{SU(3)}$ structure constants $f_{abc}$ are defined by
$$[\lambda^a,\lambda^b] = 2i f^{abc} \lambda^c,$$
with $\lambda^a$ being the Gell-Mann matrices. In three different books, I find its ...
- 103
3
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47
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Topology active subgroup for the QCD vacuum
I've been reading about the nontrivial topological structure of the QCD vacuum and, when studying the different equivalence classes created by the pure gauge fields, all papers say that it is possible ...
- 96
2
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0
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105
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Symmetry group of QCD
In "Remarks on the chiral phase transition in chromodynamics" (1984) by Pisarski and Wilczek it is stated that the (classical) global flavor symmetry is $SU(2)\times SU(2) \times U_A(1)$ ...
- 861
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1
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183
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Is $SU(3)$ (and not $U(3)$) the symmetry group of color interactions because $U(1)$ is already used for EM?
I have already seen this question. It was answered that $U(3)$ can be decomposed into $SU(3) \times U(1)$, and $U(1)$ is already used for the EM interaction. Still, I wonder why the EM interaction ...
2
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1
answer
123
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What is the reason for $U(3)_{L} \times U(3)_{R} = U(1)_{V} \times U(1)_{A} \times SU(3)_{L} \times SU(3)_{R}$?
I am studying the QCD chiral symmetry, and by considering the $u$,$d$,$s$ quarks massless, the Lagrangian
\begin{equation}
\mathcal{L} = \sum_{i = u,d,s} \bar{q}_{k}i \gamma^{\mu}D_{\mu}q_{k}
\end{...
- 858
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How to decompose tensor products of $SU(3)$ representations? [duplicate]
Formally, one can arrange the quark flavors in a $SU(n)$ fundamental representation. One can then do tensor products for flavor and spin to construct other representations like baryons and mesons. An ...
- 11
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83
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How does the electroweak interaction and QCD form $SU(2)$ and $SU(3)$?
I'm trying to get a foothold into quantum field theory from a mathematical background. I see the use of $SU(2)$ and $SU(3)$ in gauge theory and wonder the following questions to help me bring QFT ...
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