All Questions
Tagged with quantum-chromodynamics representation-theory
43
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
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
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
$$
\{T^A,T^{B}\} = \frac{1}{d}\delta^{AB}\cdot1\!\!1_{d} +...
- 609
12
votes
2
answers
2k
views
$SU(3)$ vs $SO(3)$ color gauge
I have kind of a dumb question: what would happen if the color gauge group is $SO(3)$ instead of $SU(3)$, assuming there are still colors and physical states are still color singlets? Will we e.g. get ...
- 175
12
votes
1
answer
1k
views
How many colors really are there in QCD?
In abelian gauge theory (electrodynamics), the matter fields transform like (please correct me if I am wrong)
$$
|\psi\rangle\rightarrow e^{in\theta(x)}|\psi\rangle\tag{1}
$$
under a gauge ...
- 133
11
votes
1
answer
3k
views
Decomposing a Tensor Product of $SU(3)$ Representations in Irreps
Can somebody explain in a simple way why, talking about representations $$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,$$ with $T^a$ being the generators of the group $\mathrm{SU}(3)$. They are usually written out in a very ...
- 109
7
votes
1
answer
276
views
What is the mathematical motivation for complexifying momenta in BCFW?
One of the first steps in obtaining the on-shell BCFW recursion relations is complexifying the momenta of the external particles. Now complexifying things is not unprecedented (the dispersion program ...
- 1,124
5
votes
2
answers
664
views
Quark model extension to all six flavors
Gell-Mann's $SU(3)$ quark model is extremely successful at describing the bound states of the three light quarks $u,d,s$. The bound states fall neatly into the irreducible representations of $\...
5
votes
1
answer
1k
views
Permissible combinations of colour states for gluons
My lecturer has said that there are 8 types of gluons (I'm assuming that the repetition of $r\bar{b}$ is a typo that is meant to be $r\bar{g}$)
$$r\bar{b}, b\bar{r}, r\bar{g}, g\bar{r}, g\bar{b}, b\...
- 205
4
votes
3
answers
1k
views
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
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
3
votes
2
answers
2k
views
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
3
votes
1
answer
195
views
Why can gluino (superpartner of gluon) have a Majorana mass?
I read in a paper by Scott Willenbrock that gluinos can have a Majorana mass although they have SU(3) color symmetry. The explanation was that gluinos transform under the adjoint representation which ...
- 812
3
votes
2
answers
313
views
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