All Questions
22
questions
0
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2
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122
views
Is there any physical reason behind the choice of Lie group in a Yang-Mills theory?
A Yang-Mills theory can be constructed for any Lie group that is compact and semisimple. The motivation behind this is discussed in this question. Is there any physical reason we choose $SU(3)$ or $U(...
- 3,350
0
votes
2
answers
76
views
Difference between $ SU(3)$ and $ SU(3)_c $ group
I am reading quark model. I don't understand what's the meaning of a color $SU(3)$ or $SU(3)_c$ group and how it differs from a general $SU(3)$ group. Please elaborate.
- 377
0
votes
1
answer
185
views
Is $SU(3)$ (and not $U(3)$) the symmetry group of color interactions because $U(1)$ is already used for EM?
I have already seen this question. It was answered that $U(3)$ can be decomposed into $SU(3) \times U(1)$, and $U(1)$ is already used for the EM interaction. Still, I wonder why the EM interaction ...
0
votes
0
answers
83
views
How does the electroweak interaction and QCD form $SU(2)$ and $SU(3)$?
I'm trying to get a foothold into quantum field theory from a mathematical background. I see the use of $SU(2)$ and $SU(3)$ in gauge theory and wonder the following questions to help me bring QFT ...
- 101
2
votes
0
answers
94
views
Is there any progress in the study of the relationship between Rubik's cube and quark?
After Golomb discovered the relationship between Rubik's cube and quark, Anthony E. Durham improved it. Is there a link to Anthony E. Durham's work? May be the principal bundles can explain the ...
2
votes
1
answer
171
views
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 ${\...
- 26.8k
0
votes
0
answers
221
views
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,
$$
\mathbf{3} \otimes \mathbf{\bar{3}}= \mathbf{8} \...
1
vote
1
answer
122
views
An invariant of the gauge group $G$ that is totally symmetric with three indices in the adjoint representation
In Ch.19 of the textbook An Introduction to Quantum Field Theory by Peskin and Schroeder, on P.680 the property of a quantity
$$\mathcal{A}^{abc}=\mathrm{tr}\left[t^a\{t^b,t^c\}\right]\tag{19.132}$$
...
- 962
1
vote
1
answer
77
views
What prohibits fundamental fermions transforming like the $6$ and $6^*$ IRR's of $SU(3)$?
The lowest IRRs of SU(3) are 3,3* (the fundamental reps), 6,6*, and 8 (the adjoint rep). The quark fields are chosen to transform as 3, 3*, and the gluons as 8 under SU(3), but there is no ...
- 417
1
vote
0
answers
137
views
Why is $SU(3)$ and not $U(3)$ the correct gauge symmetry? [duplicate]
If quarks come in three colours $r$, $g$ and $b$ than (neglecting all other quantum numbers and spacial freedom for now) a state of a quark would be a vector in $\mathbb{C}^3$.
If we are now looking ...
- 123
2
votes
2
answers
110
views
The distinctions between $\mathrm{U}(1)$ and $\mathrm{SU}(3)$ massless bosons
The force carrier particles that mediate the electromagnetic, weak, and strong interactions are called gauge bosons. It is known that the gauge bosons in EM force and strong force are both massless.
...
- 196
1
vote
0
answers
50
views
The remained global flavor symmetries of massless quarks after gauging electromagnetic $U(1)$
For $N_f$ numebr of massless quarks, we know that there are global symmetries
$$
\frac{SU(N_f)_L \times SU(N_f)_R \times U(1)_V}{Z_{N_f}}
$$
here $U(1)_V$ is the same as $U(1)$-Baryon number ...
- 4,336
5
votes
2
answers
664
views
Quark model extension to all six flavors
Gell-Mann's $SU(3)$ quark model is extremely successful at describing the bound states of the three light quarks $u,d,s$. The bound states fall neatly into the irreducible representations of $\...
11
votes
0
answers
445
views
Is the QCD Lagrangian without a $\theta$-term invariant under large gauge transformations?
In his book "Quantum field theory", Kerson Huang states that we need to add the term $$\frac{i\theta}{32\pi^2}G_{\mu\nu}^a \tilde{G}_{\mu\nu}^a$$ to the Lagrangian, to make it invariant under large ...
- 10.1k
4
votes
2
answers
634
views
A Question about a $U(1)_{B-L}$
I know I can write the QCD lagrangian like this:
$$ \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