All Questions
Tagged with quantum-chromodynamics group-theory
62
questions
1
vote
0
answers
683
views
SU(3) adjoint representation's invariant tensors
Considering a complex scalar field $\varphi^a$ that transform in the adjoint representation (8) of SU(3).
A quartic interaction term SU(3) invariant is
$$\lambda C^{abcd}\varphi^{\dagger a} \varphi^...
- 21
0
votes
0
answers
456
views
Non-singlet and singlet flavor combination [duplicate]
In the perturbative QCD, specific partonic distribution functions (pdf) linear combination is called "flavor singlet" or "flavor nonsinglet" combination.
What is the combination, and why are they ...
- 857
4
votes
2
answers
634
views
A Question about a $U(1)_{B-L}$
I know I can write the QCD lagrangian like this:
$$ \mathcal{L} = (i\bar{q}_{R} \gamma_{\mu}\partial_{\mu} {q}_{R} + i\bar{q}_{L}\gamma_{\mu}\partial_{\mu} {q}_{L}) + \text{other terms} $$
When ...
- 558
3
votes
1
answer
270
views
How many glueballs are there?
As I understand there are eight types of gluons (linear combinations of color/anticolor pairs with varying amplitudes) which can combine (for very short periods) to form glueballs. If there were no ...
- 756
2
votes
1
answer
376
views
Why do we say that gluons carry color charge?
We know that gluons are Lie algebra $su(3)$-valued one-form fiels $A_{\mu}$. And because of $[A_\mu,A_\nu]$ does not vanish generally for the non-Abelian case, gluons have self-interactions. Now how ...
- 3,691
15
votes
3
answers
6k
views
The anticommutator of $SU(N)$ generators
For the Hermitian and traceless generators $T^A$ of the fundamental representation of the $SU(N)$ algebra the anticommutator can be written as
$$
\{T^A,T^{B}\} = \frac{1}{d}\delta^{AB}\cdot1\!\!1_{d} +...
- 609
2
votes
1
answer
153
views
QCD Color Structure relation [closed]
i want to proof the following relation :
\begin{equation}
t^a t^b \otimes t^a t^b = \frac{2}{N_C} \delta^{ab} \mathbb{1} \otimes \mathbb{1} - \frac{1}{N_C} t^a \otimes t^a
\end{equation}
Right now I ...
- 379
3
votes
1
answer
416
views
Different ways of derivation of Gell-Mann-Okubo mass formula
Recently my teacher told me that there are many ways of deriving the Gell-Mann-Okubo mass formula by using group representation theory (by using dynamical group etc). Where can I read about these ways?...
2
votes
0
answers
56
views
Measure of interaction of two quarks and Casimir operators [closed]
Let's have two quarks, which refers to representations of $r_{1}$ and $r_{2}$ of color symmetry group. They create bounded state which refers to the representation $r$.
There is a statement that ...
user8817
1
vote
0
answers
118
views
Uncharged Gluon Representation
I'm currently learning for an exam and in an old exam the question was posed:
If Gluons were uncharged, under which representation would they transform?
The ...
- 10.1k
5
votes
1
answer
672
views
Group theoretical reason that Gluons carry color-charge and anti-colorcharge
I was wondering how it is possible to see from the $SU(3)$ Gauge Theory alone that Gluons carry two charges colors: $g\overline{b}$ etc.
Some background:
The W-Bosons (pre-symmetry breaking) form an ...
- 10.1k
6
votes
0
answers
239
views
From $U(3)$ to $SU(3)\times U(1)$ Color symmetry. There is a "gluon" photon-like?
Suppose that $U(3)$ was the gauge group. We can decompose this as
$U(3)=U(1)\times SU(3)$,
which implies that in addition to the $SU(3)$ that has eight generators corresponding to eight gluons, there ...
- 558
14
votes
2
answers
2k
views
Why $SU(3)$ and not $U(3)$?
Is there a good reason not to pick $U(3)$ as the colour group? Is there any experiment or intrinsic reason that would ruled out $U(3)$ as colour group instead?
- 558
2
votes
2
answers
696
views
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?
- 253
9
votes
2
answers
2k
views
Why is $SU(3)$ chosen as the gauge group in QCD?
Why is $SU(3)$ chosen as the gauge group. Why not $U(3)$? Why does it even have to be unitary?
- 2,147