All Questions
Tagged with beyond-the-standard-model representation-theory
25 questions
1
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0
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51
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How to know the minimal coupling and how to find eigenvalues of arbitrary representations?
I'm dealing with the following problem. In a $ SU(3)_L\times U(1)_X$ model, the scalar representation content accomodates the following anti-sextet
$$
S \equiv \begin{pmatrix}
\sigma_1^0 & \frac{...
- 1,782
4
votes
0
answers
75
views
Zee Chapter VII.5: Can the fermion $10$ be the composite of fermion $5^*$?
In Zee Chapter VII.5 QFT book:
He showed that the standard model fermions form $5^*$ and $10$ representations of $SU(5)$:
$$
5^* \oplus 10.
$$
In particular, the $10$ is the anti-symmetric matrix ...
- 4,376
5
votes
0
answers
99
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Figure of $SO(10)$ grand unified theory in $E_6$ from Wikipedia
In this figure from Wikipedia, it shows that the representations of particles of $SO(10)$ grand unified theory, their patterns of charges for particles in the $SO(10)$ model, rotated to show the ...
- 4,376
1
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0
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116
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Figure of $SO(10)$ grand unified theory from Wikipedia
In this Figure from Wikipedia, it shows that the representations of particles of $SO(10)$ grand unified theory, representations as numbers labeled in several axes.
Descriptions: The patterns of
weak ...
- 4,376
2
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0
answers
40
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$ (5^* \times 5^*)_{asym}={10}$ in A. Zee's book p.409 versus PDG Sec.114
What is the mathematical or physical way to understand why the 4th and 5th components in the Georgi Galshow SU(5) model has the SU(2) doublet $(1,2,-1/2)$:
$$
\begin{pmatrix}
\nu\\e
\end{pmatrix}
$$
...
- 4,376
5
votes
0
answers
160
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$\rm SO(10)$ grand unified model restores the parity symmetry lost in $\rm SU(5)$ model
It is said in Lie Algebras in Particle Physics 2ed - From Isospin to Unified Theories (Georgi, 1999) p.285, Georgi said that
$\rm SO(10)$ grand unified model restores the parity symmetry that was ...
- 4,376
1
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0
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37
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Light composite fermion as a bound state formed by $SU(4)$ gauge force attractions
In this paper https://inspirehep.net/literature/152400, in eq.(3.4), it claims that
the MAC (most attractive channel) in $SU(4)$ gauge theory will attract
fermions in $[1]_4$
and
fermions in $[3]_4$
...
- 4,376
2
votes
0
answers
196
views
Why isn't the triplet representation of $SU(2)$ symmetric?
By the Young Tableaux construction, a triplet of $SU(2)$ (diagramatically, two boxes side by side) is supposed to be a two indices symmetric tensor.
However, one of the most known and minimal ...
- 1,782
2
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0
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136
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Lectures by Susskind versus Zee on the ${\rm SU}(5)$ grand unified theory notations
I was comparing two lectures about ${\rm SU}(5)$ grand unified theory.
a lecture of Susskind
He showed how to write
$$
(5 \times 5)_{asym}=\bar{10}
$$
as
a lecture of Zee showed how to write
$$
(\...
- 4,376
3
votes
0
answers
32
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Neutrino flavor models from irreducible representations of discrete groups [duplicate]
I am starting ph.D in neutrino physics-ph. I've read some papers on discrete symmetries and neutrino mass models. Neutrino flavor models are built using irreducible representations of discrete groups, ...
23
votes
4
answers
3k
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Why do all fields in a QFT transform like *irreducible* representations of some group?
Emphasis is on the irreducible. I get what's special about them. But is there some principle that I'm missing, that says it can only be irreducible representations? Or is it just 'more beautiful' and ...
- 333
0
votes
1
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60
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How do we know the group property of a new particle?
Suppose I have a particle $W'$ which can decay into $\mu$ and $\nu_{\mu}$ and $e$ and $\nu_{e}$.
Suppose we know such new gauge bosons come from some additional gauge group added to the Standard ...
1
vote
1
answer
237
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Constraints on RH component of fermion triplet under $SU(2)_L$
Consider a fermion $\chi$ whose left-handed part is in a triplet representation of $SU(2)_L$:
$$ \chi_{L} = (\chi^1,\chi^2,\chi^3)_L^{\ \ \text{T}}. $$
The charged current of $\chi_L$ (i.e. its ...
- 1,168
2
votes
1
answer
276
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Can $E_8 \times E_8$ contain the standard model?
I know $E_8$ by itself can't be gauge group because it has no complex representation and so would not be chiral. But assuming the existence of mirror matter which also would have $E_8$ gauge group ...
user84158
2
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3
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3k
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Given the transformation of $SU(2)$ triplet $\vec{\phi}$ how to find the transformation of ${\Phi}\equiv\vec{\phi}\cdot\vec{\tau}$?
Given the transformation of a $SU(2)$ triplet $\vec\phi$ $$\phi\to \exp{(-i\vec{T}\cdot\vec{\theta})}~\vec\phi\tag{1}$$ (in the question here by @physicslover) how does obtain the transformation of $\...
- 27.2k
9
votes
1
answer
2k
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How to decompose the representation of $\rm SU(5)$?
This question comes from Srednicki's textbook "Quantum Field Theory". On pages 514-515, it states:
Under the unbroken $\rm SU(3)\times SU(2) \times U(1)$ subgroup, the $5$ representation of ...
- 1,673
4
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0
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What is the meaning of SU(2) triplet scalar field? [closed]
The following is an about a Left-Right Symmetric model.
$SU(2)\otimes SU(2)$ $(2\otimes 2=3\oplus 1)$ will generate a triplet, which in Left-Right Symmetric model is $$\vec{\Delta}=\begin{pmatrix}\...
- 277
1
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1
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467
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Correct Yukawa Term with a SU(2) Higgs Triplet?
Given $SU(2)$ doublet fermions $\Psi^1$ and $\Psi^2$ and a $SU(2)$ triplet Higgs $H$, how does the correct Yukawa term look like in tensor notation?
Schematically, we have
$$ 2 \otimes 2 \otimes 3 \...
- 10.3k
3
votes
0
answers
211
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What does complexification mean for our particles in physics?
As gauge group let's consider the popular $SO(10)$ group.
The fundamental representation $\pi$ of the corresponding Lie algebra $\mathfrak{so}(10)$ is $10$ dimensional
$$ \pi: \mathfrak{so}(10) \...
- 10.3k
0
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0
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77
views
Why is the tensor product $n \otimes n = 1$ for $SO(n)$ not the usual scalar product?
For concreteness let's consider $SO(4)$.
The quantum numbers for the four states in the fundamental representations are (schematically)
$$ (1, 1) ,(-1, 1) ,(1, -1) ,(-1, -1 )$$
thus
$$ 4= \...
- 10.3k
3
votes
1
answer
203
views
How to find the remaining subgroup after some linear combination of Higgs fields gets a VEV?
This is a follow-up question to this question.
How can I compute which generators remain unbroken when a linear combination of Higgs fields $a \Phi_1+ b\Phi_2$ get a vev?
If I compute the unbroken ...
- 10.3k
3
votes
1
answer
201
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Symmetry breaking to a special subalgebra?
This is a follow-up to my question here.
For regular subalgebras of some group's Lie algebra the root system of the subalgebra is a subset of the root system of the original's group algebra. In other ...
- 10.3k
1
vote
1
answer
410
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How to find the remaining subgroup after some Higgs field gets a VEV?
Say we have a group $G$ and a set of Higgs fields in a representation $R$ of $G$. One of the Higgs fields in $R$ gets a VEV, how can I determine the remaining subgroup after this symmetry breaking?
...
- 10.3k
5
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2
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751
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Why do decompositons like $16 \otimes 16 = 10 \oplus 120 \oplus 126$ tell us which Higgs representations we can use?
EDIT: I found an answer, which I do not understand: In Gürsey - Symmetry breaking patterns in E6 he writes: " Because of Fermi-Dirac statistics of fermions they must occur in the symmetric part of ...
- 10.3k
5
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1
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Higgs Mechanism
In Higgs mechanism, we take the combination of LH $SU(2)$ doublet and RH singlet along with Higgs doublet so that the overall weak hypercharge and weak isospin is zero to be $SU(2) \times U(1)$ ...
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