All Questions
Tagged with group-theory particle-physics
91
questions
3
votes
1
answer
58
views
Measurable effects of the global structure of the SM
It is known that the Lie algebra of the SM is
$$
\mathfrak{su}(3)\oplus \mathfrak{su}(2)\oplus \mathbb{R}\,,
$$
so that the Lie group is
$$
G_{\text{SM}} = \dfrac{SU(3)\times SU(2) \times U(1)}{\Gamma}...
- 1,611
3
votes
0
answers
35
views
Why a scalar particle with momentum orbit $\mathcal{O}_p$ is irreducible?
Let $G$ be a Lie group and $A$ a finite dimensional vector space. A scalar particle with momentum orbit $\mathcal{O}_p$ is a represenation $T: G\ltimes A\to GL(L^2 (\mathcal{O}_p,\mu,\mathbb{C}))$ ...
- 374
0
votes
1
answer
103
views
Custodial symmetry of the standard model symmetry group $SU(2)_L \times SU(2)_R$
I am studying the standard model including the Higgs sector and electroweak interactions. Here, all of my terms have their usual meanings. Therefore my symmetry group is $SU(2)_L \times SU(2)_R \times ...
- 51
22
votes
2
answers
2k
views
Have all the symmetries of the standard model of particle physics been found?
Background
The standard model of particle physics is entirely determined by writing down its Lagrangian or, equivalently, writing down the corresponding system of PDEs.
Every set of PDEs has a ...
- 323
0
votes
0
answers
47
views
Why are the expressions of the Skyrme Model related with a kinetic and a mass term?
I was reading about the Syrme Model Lagrangian,
$$
\mathcal{L} =-f^2_\pi/4 Tr(L_\mu L^\mu) + 1/32e^2 Tr([L_\mu,L_\nu]^2)- \frac{\mu^2}{2} Tr(1-U)
$$
where $L_\mu=U^\dagger \partial_\mu U$. I've read ...
- 161
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
1
vote
0
answers
45
views
Why are the weight vectors corresponding to the raising and lowering operators given by the formula $\bar{t_{1}}- \bar{t_{2}}$?
I am reading Robinson's particle physics paper part-I which is available in the public domain
here, particularly the theory of SU(3) Lie Groups. Page 63 of the text states that,
Now, repeating ...
- 11
1
vote
1
answer
215
views
Do the Casimir operators for $su(3)$ algebra of particle physics carry any physical meaning?
For the $su(2) $ algebra of angular momentum, the eigenvalues of the Casimir operator, $\hat{J^2}$, represents the square of the total angular momentum of a system. The $su(3)$ algebra has rank 2 and ...
- 11.8k
2
votes
2
answers
181
views
How can different representations of the same group correspond to different particles?
When I first learned group theory in the context of quantum mechanics, I got it into my head that a group was the unification of different "transformation actions" that ultimately have the ...
- 525
1
vote
0
answers
107
views
Finite quotient of standard model group [closed]
In chapter three, p. 31, of this paper (https://arxiv.org/abs/0904.1556) Baez and Huerta show that the standard model's structure group contains, in a sense, superfluous parts.
They show that one can ...
- 357
1
vote
1
answer
100
views
If an $SU (2)$ isospin transformation converts a proton to a neutron, how does a pion transform under the same transformation?
I read in a particle physics note that if an $SU(2)$ isospin transformation makes $p\rightarrow n$ then under the same transformation pions go like $\pi^+ \rightarrow\pi^-$. I'm assuming that this ...
- 126
1
vote
2
answers
98
views
By what transformation are particles of a multiplet related to each other?
My question is about the relation between the members of the members of a multiplet, for example the baryon-Decuplet or one of the Baryon-Octets. By what transformation are they related? Are they ...
- 63
1
vote
1
answer
68
views
Can I still use the table of Clebsh-Gordan coefficients if isospin isn't conserved, to calculate the branching ratio?
the title is basically everything. For example, the interaction $\Lambda^0 \rightarrow \Sigma^+ + \pi^-$ or $\Lambda^0 \rightarrow \Sigma^0 + \pi^0$. Isospin isn't conserved but the interaction is ...
- 25
1
vote
2
answers
573
views
Meaning of $SU(n)$ and $SO(n)$ symmetry groups in particle physics
I am currently self studying introductory particle physics using An Introduction to Elementary Particles by David J. Griffiths. I was reading Chapter 4 of this textbook which deals with the topic of ...
- 498
1
vote
1
answer
234
views
How to construct matrix representations of particle multiplets?
Similarly to how the SU(2)-triplet W-bosons can be written as a vector with three components $\big(W^1, W^2, W^3\big)^T$ or as a 2x2 matrix by contracting with the Pauli matrices $\big(\textbf{W} = W^...
- 13