All Questions
Tagged with quantum-chromodynamics representation-theory
43
questions
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77
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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
3
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0
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134
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What is the physical meaning of Lie congruence classes?
Any weight $\lambda$ characterising a representation of $\mathfrak{su}(N)$ is an element of one of the $N$ congruence classes defined by (ref.1)
$$
\lambda_1+2\lambda_2+\cdots+(N-1)\lambda_{N-1}\quad\...
2
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1
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263
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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
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630
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"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
1
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2
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1k
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Breaking of $SU(3)$ symmetry by bi-fundamental representation
Are there any general theorems which fix the possible symmetry breaking patterns of Lie groups (such as $SU(3)$) by vacuum expectation values of fields in specific representations (such as the quark ...
- 1,783
4
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$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
12
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2
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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
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297
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Formal definition of gauge field and spinors in QFT
I am trying to pin down what spaces a spinor and gluon gauge field exactly occupy. I know that the spinor is a quantity $\psi_{i\alpha f}(\vec x, t)$ where
$i$ is a color index in the fundamental ...
- 8,439
5
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2
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664
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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 $\...
3
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195
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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
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Why does the $U(2n)$ flavor symmetry break down to a $U(1)$ group and an $SU(2n)$ group?
I am studying quantum field theory using Srednicki's textbook. Problem 83.1 is:
Suppose that the color group is $G_C=SO(3)$ rather than $SU(3)$, and that each quark flavor is represented by a Dirac ...
- 1,653
2
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1
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2k
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How are the generators of $\mathrm{SU}(3)$ represented on the gluon space?
I was watching some new lectures on QCD from Colorado and I have a few questions about what I heard:
The $\lambda^a_{ij}$ are generators of $\mathrm{SU}(3)$ in the fundamental representation so are $...
- 3,569
2
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1
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688
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What is the effect of the Gell-Mann matrices on color antiparticles?
I'm studying QCD and I can't understand how exactly are defined the color antiparticles. Indeed, we have the particle color triplet $(r,g,b)$. With the usual SU(3) algebra, we define the 8 Gell-Mann ...
- 2,296
0
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2
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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
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683
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SU(3) adjoint representation's invariant tensors
Considering a complex scalar field $\varphi^a$ that transform in the adjoint representation (8) of SU(3).
A quartic interaction term SU(3) invariant is
$$\lambda C^{abcd}\varphi^{\dagger a} \varphi^...
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