All Questions
Tagged with quantum-chromodynamics representation-theory
43
questions
1
vote
1
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55
views
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
2
votes
1
answer
433
views
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
0
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0
answers
242
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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 $$...
user242231
4
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3
answers
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Is the concept of bicolored gluons mathematically precise/meaningful? Please explain
Each flavour of quark carries a colour quantum number: red, green or blue. I know what it means mathematically. But elementary textbooks (e.g, particle physics by Griffiths) also say that gluons are ...
- 11.8k
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2
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91
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Quantum chromodynamics - why are there no $rrb$ or $ggr$ terms?
$$\Psi_{colour}^{qqq} = \frac{1}{\sqrt{6}}(rgb + gbr + brg -grb - rbg - bgr)$$
My lecturer stated that there cannot be any $rrb$ or $ggr$ terms in the expression above. I would like to understand what ...
- 13
2
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2
answers
68
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How do we understand the ${\bf 3}$ of $Q_L({\bf 3}, {\bf 2})_{1/3}$?
A left-handed quark doublet of the Standard Model is specified as $Q_L({\bf 3}, {\bf 2})_{1/3}=(u,d)^T$. I have a problem understanding this quark doublet as a triplet of ${\rm SU}(3)$. Any help? I ...
- 11.8k
12
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1
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How many colors really are there in QCD?
In abelian gauge theory (electrodynamics), the matter fields transform like (please correct me if I am wrong)
$$
|\psi\rangle\rightarrow e^{in\theta(x)}|\psi\rangle\tag{1}
$$
under a gauge ...
- 133
1
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0
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How to decompose tensor products of $SU(3)$ representations? [duplicate]
Formally, one can arrange the quark flavors in a $SU(n)$ fundamental representation. One can then do tensor products for flavor and spin to construct other representations like baryons and mesons. An ...
- 11
2
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2
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284
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Do the “$SU(3)$ colors” live in a 3-dimensional vector space?
Previously I asked a question about the visualized colors:
Do the "colors" live in a 3-dimensional vector space?
(My earlier question is unfortunately closed)
Now I like to ask the “$SU(3)$ ...
- 4,336
3
votes
2
answers
309
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Normalisation of QCD Lagrangian
In QCD, and more generally in representations of $\mathfrak{su}(N)$, there is a freedom to choose the normalisation of the generators,
$$
\mathrm{Tr} \, \left[R(T^a) R(T^b)\right] = T_R \delta^{ab}.\...
- 264
2
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1
answer
170
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Physical significance of the reality of an ${\bf N}$ representation: how the nature of interactions is affected?
Background The fundamental representation of ${\rm SU(N)}$ is denoted by ${\bf N}$ and the conjugate of the fundamental is denoted by ${\bar{\bf N}}$. If the representation ${\bf N}$ is related to ${\...
- 26.7k
0
votes
0
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217
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What is the application of dimension $6$ representation of $SU(3)$ in particle physics?
As we know, the $uds$ transforms in fundamental representations of $SU(3)$. It has the antifundamental partner. According to representation theory,
$$
\mathbf{3} \otimes \mathbf{\bar{3}}= \mathbf{8} \...
3
votes
2
answers
2k
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Confusions with gluons. How many of them are there?
Gluons are bicolored objects. They are made out of one color and one anticolor. Therefore, there seems to be nine possible states $r\bar{r},r\bar{b},r\bar{g},b\bar{r},b\bar{b},b\bar{g},g\bar{r},g\bar{...
- 11.8k
0
votes
1
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146
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Clarification about confinement of colour charged objects
In lecture today we were reviewing the QCD lagrangian, and discussing hadronic wavefunctions. My lecturer said that QCD alone allows for states of colored hadrons, however because we do not see ...
- 1,117
8
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1
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$\mathfrak{su}(3)$ structure constants
The $\mathfrak{su}(3)$ structure constants $f^{abc}$ are defined by $$[T^a,T^b] = i f^{abc} T^c,$$ with $T^a$ being the generators of the group $\mathrm{SU}(3)$. They are usually written out in a very ...
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