All Questions
Tagged with quantum-chromodynamics representation-theory
11
questions
29
votes
1
answer
7k
views
Mathematically, what is color charge?
A similar question was asked here, but the answer didn't address the following, at least not in a way that I could understand.
Electric charge is simple - it's just a real scalar quantity. Ignoring ...
- 1,505
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
$$
\{T^A,T^{B}\} = \frac{1}{d}\delta^{AB}\cdot1\!\!1_{d} +...
- 609
22
votes
4
answers
14k
views
Trace and adjoint representation of $SU(N)$
In the adjoint representation of $SU(N)$, the generators $t^a_G$ are chosen as
$$ (t^a_G)_{bc}=-if^{abc} $$
The following identity can be found in Taizo Muta's book "Foundations of Quantum ...
- 1,701
11
votes
1
answer
3k
views
Decomposing a Tensor Product of $SU(3)$ Representations in Irreps
Can somebody explain in a simple way why, talking about representations $$3\otimes3\otimes3=1\oplus8\oplus8\oplus10~?$$
Here $3$ and $\bar{3}$ are the fundamental and anti-fundamental of $SU(3)$, in ...
- 353
8
votes
1
answer
5k
views
$\mathfrak{su}(3)$ structure constants
The $\mathfrak{su}(3)$ structure constants $f^{abc}$ are defined by $$[T^a,T^b] = i f^{abc} T^c,$$ with $T^a$ being the generators of the group $\mathrm{SU}(3)$. They are usually written out in a very ...
- 109
5
votes
1
answer
1k
views
Permissible combinations of colour states for gluons
My lecturer has said that there are 8 types of gluons (I'm assuming that the repetition of $r\bar{b}$ is a typo that is meant to be $r\bar{g}$)
$$r\bar{b}, b\bar{r}, r\bar{g}, g\bar{r}, g\bar{b}, b\...
- 205
4
votes
1
answer
2k
views
$SU(3)$ Color Symmetry
I have following (maybe a bit general) question about the $SU(3)$-symmetry of color by quarks:
If I consider the analogy to the $SU(2)$-symmetry of isospin $I$ crucially it concers the conservation ...
- 1,395
2
votes
2
answers
288
views
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
2
votes
1
answer
263
views
axial anomaly for adjoint fermion v.s. fundamental fermion
It is known that the axial anomaly (chiral anomaly, the left L- right R) shows that $U(1)_A$-axial symmetry is not a global symmetry at quantum level.
In particular, one can consider the (1) ...
- 4,336
1
vote
1
answer
630
views
"Color charge" of the adjoint fermion?
What kind of "color charge" does the adjoint fermion carry?
Let us consider the SU(N) gauge theory. The gauge field is in the adjoint representation (rep).
Well-Konwn: If the fermion is in SU(N) ...
- 4,336
0
votes
2
answers
1k
views
Why are 3 colors used in QCD?
The mapping of strong charge to RGB left me believing that there are only 3 conserved quantities in QCD. I recently came to the understanding that there are in fact 8 conserved quantities, as ...
- 403