All Questions
Tagged with group-theory symmetry-breaking
75
questions
3
votes
2
answers
111
views
Does all symmetry breaking have corresponding unitary group?
In high energy physics. Symmetry breaking like electroweak's has corresponding $SU(2)\times U(1)$ unitary gauge group broken down to $U(1)$. Does it mean all kinds of symmetry breaking (even low ...
- 425
0
votes
1
answer
103
views
Custodial symmetry of the standard model symmetry group $SU(2)_L \times SU(2)_R$
I am studying the standard model including the Higgs sector and electroweak interactions. Here, all of my terms have their usual meanings. Therefore my symmetry group is $SU(2)_L \times SU(2)_R \times ...
- 51
0
votes
1
answer
144
views
$SU(5)$ Gauge Field Theory, symmetry breaking
If I start with an $SU(5)$ gauge group and discover that the vacuum is preserved only by matrices of the form $G$
$$\begin{bmatrix}
A & 0 \\
0 & B \\
\end{bmatrix}$$
where ...
- 3
0
votes
1
answer
62
views
Perturbation Theory with no symmetry breaking?
I was learing about group theory in QM and stable about symmetry breaking. I find it very interesting and search some stuff and even looked on wikipedia and found this: https://en.wikipedia.org/wiki/...
1
vote
0
answers
123
views
Question about $E_8$ symmetry breaking and hypercharge formula
Most $E_8$ gauge theories follow this breaking chain:
$$E_8 \rightarrow E_6 \times SU(3)_{Gen}.$$
How does the $E_6 \times SU(3)$ group break down through $SO(10)$, the Pati-Salam Model or the Minimal ...
- 69
1
vote
1
answer
214
views
Symmetry groups breaking for the lagrangian of two complex scalar fields
Suppose we have a generic non-interacting Lagrangian of two complex scalar fields,
\begin{align}
\mathcal{L} &= (\partial^\mu \Phi^\dagger)(\partial_\mu \Phi) - \Phi^\dagger\mathbb{M}^2\Phi \tag{1}...
- 1,783
2
votes
0
answers
50
views
Domain walls in theories of axions
I'm stuck in figuring out why some theories of axions predict the existence of domain walls.
Axions are NG bosons associated with the chiral $U(1)_{PQ}$ symmetry, which was spontaneously broken at ...
- 117
1
vote
1
answer
215
views
Goldstone bosons and spontaneous symmetry breaking in the complex triplet model
In the Standard model electroweak theory, the Higgs field is a complex doublet field, which couples to the $SU(2)$ gauge field. Suppose we replace the complex doublet with a complex triplet $\Sigma$:
$...
- 1,421
2
votes
1
answer
102
views
In QFT, are there any restrictions on spontaneous breaking $G\to H$, due to "spontaneity"?
For simplicity, let us restrict to the spontaneous breaking of global symmetries. Given any pair of groups $G\supset H$, is it always possible to find a $G$-invariant Lagrangian that gives a QFT such ...
- 213
2
votes
1
answer
61
views
Which order multiplet of a given $SU(N)$ is real or complex?
I am studying the $SU(2)$ symmetric Lagrangian in particle physics.
$${\mathcal{L}} = (\partial_\mu \Phi)^\dagger (\partial^\mu \Phi) - (\mu^2 \Phi^ \dagger \Phi + \lambda (\Phi^ \dagger \Phi)^2).$$
...
- 399
0
votes
1
answer
249
views
What's the difference between the global transformations of $SU(2)$ and $U(1)$?
I am studying the spontaneously broken global non-Abelian symmetry. Suppose we have an $SU(2)$ doublet of bosons $\Phi = (\phi^+, \phi^0)^T$, with Lagrangian density
$$
\mathcal L = (\partial_\mu\Phi^\...
- 1,783
3
votes
1
answer
224
views
How can we determine which subgroup remains unbroken after spontaneous symmetry breaking for $SU(2)\times U(1)$ symmetry?
Consider an $SU(2)$ doublet of bosons $\Phi = (\phi^+, \phi^0)^T$, where the complex scalar field $\phi^+$ destroys positively charged particles and creates negatively charged ones, and the complex ...
- 1,783
4
votes
2
answers
318
views
What is meant by the statement that Wigner-Weyl is linear realization and Nambu Goldstone is nonlinear realization?
In a paper, "Nonlinear Realization of Global Symmetries" by Zhong-Zhi Xianyu, I see the line
"There are basically two ways of symmetry realization in Hilbert space. One is such that ...
1
vote
1
answer
105
views
Number of Goldstone modes when the symmetry is broken?
I am studying lecture notes on Groups and Representations by Prof. Andre Lukas. I am unable to completely understand notesnd the examples worked out in the symmetry-breaking application section (pages ...
- 317
1
vote
1
answer
432
views
What interaction breaks $SU(3)$ flavor symmetry?
I know that flavor symmetry is only approximate, broken since the u,d, and s quarks have different masses. Also that trying to extend $SU(3)$ symmetry to $SU(4)$, $SU(5)$, or $SU(6)$ symmetry is ...
- 163