All Questions
12
questions
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83
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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
3
votes
2
answers
313
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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,
$$
\mathrm{Tr} \, \left[R(T^a) R(T^b)\right] = T_R \delta^{ab}.\...
- 264
2
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0
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68
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Abelian theories with more than one charge
I have a question about the non-abelian character of QCD. In order to write a gauge-invariant Lagrangian, there must be a term with the strength tensor $X^{\mu\nu}_{a}X_{\mu\nu}^{a}$ where
$$
X^a_{\mu\...
1
vote
2
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746
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How does the underlying symmetry of QCD imply the allowance of a 4-gluon vertex?
Quantum chromodynamics allows for a four-gluon vertex such as this, in a diagram
Such a vertex would never be allowed in quantum electrodynamics, which has an underlying U(1) gauge symmetry.
I know ...
- 324
2
votes
1
answer
529
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$U(N)$ & $SU(N)$ : What's the conceptual difference in Gauge Theory?
I know the mathematical difference that one means $ absolutevalue(det) = 1$ and one means det = 1 (rotation) and that ones the subgroup of the other and so on.
But:
has a local/gauged $SU(3)$ ...
- 91
4
votes
1
answer
2k
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Why quarks in the fundamental and gluons in the adjoint?
I have been told that in gauge theories
“fermionic matter goes in the fundamental rep of $SU(N)$, while gauge fields go in the adjoint rep”.
I understand how this works, and for instance, in QCD,...
- 1,154
4
votes
1
answer
159
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QCD from chirally segregated, gauged $SU(3)_L \times SU(3)_R$?
There are already theory papers out there in which color $SU(3)_C$ is actually the diagonal subgroup of multiple $SU(3)$ factors. But due to a comment by @zooby, a new twist on this idea occurred to ...
- 13.1k
1
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0
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137
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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
1
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0
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50
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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
12
votes
2
answers
2k
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$SU(3)$ 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
11
votes
0
answers
445
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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
3
votes
1
answer
270
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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