All Questions
Tagged with quantum-chromodynamics representation-theory
43
questions
0
votes
0
answers
456
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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
7
votes
1
answer
276
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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
1
vote
0
answers
280
views
Names for various color indices in QCD
In Quantum Chromodynamics with $\mathrm{SU}(3)$ there are at least two types of color indices:
Indices $a$, $b$, … that index the eight generators of the group $\mathrm{SU}(3)$. In some sense they ...
- 8,439
15
votes
3
answers
6k
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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
$$
\{T^A,T^{B}\} = \frac{1}{d}\delta^{AB}\cdot1\!\!1_{d} +...
- 609
2
votes
2
answers
552
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Pentaquark spin prediction
Is there a straightforward way to see what the spin of the recently-discovered pentaquark states should be, from the representation theory of $SU(3)\times SU(2)\subset SU(6)$? I can see that from the ...
- 4,418
5
votes
1
answer
1k
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Permissible combinations of colour states for gluons
My lecturer has said that there are 8 types of gluons (I'm assuming that the repetition of $r\bar{b}$ is a typo that is meant to be $r\bar{g}$)
$$r\bar{b}, b\bar{r}, r\bar{g}, g\bar{r}, g\bar{b}, b\...
- 205
1
vote
1
answer
149
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Interpretation of vector mesons in QCD
It is well-known that scalar mesons are interpreted as pseudogoldstone bosons which is connected with spontaneous broken $SU(3) \times SU(3)$ symmetry to $SU(3) \times SU(3) / SU(3)_{chiral}$.
Is ...
- 6,564
3
votes
1
answer
416
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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
0
votes
2
answers
249
views
Quark space tensor product Vs Angular momentum space tensor product
For two triplet angular momenta states, say $J=1$ and $I=1$, if we wanna look at it in the coupled basis $F=I+J$, we use the regular Angular Momentum rules:
$$|I-J|\leq F\leq I+J,$$
and from that ...
- 3,447
22
votes
4
answers
14k
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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
29
votes
1
answer
7k
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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 ...
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