All Questions
Tagged with group-theory standard-model
121
questions
1
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0
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54
views
Do GUT's really explain parity violation?
Every book on the Standard Model introduces early on the concept of left and right-handed quantum fields, defined as
\begin{align}
(\psi_L)_{\alpha} = \left(\frac{1-\gamma_5}{2}\right)_{\alpha \beta}\...
- 131
1
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0
answers
44
views
One-Loop beta function for gauge couplings
I am currently doing my homework on Standard Model one-loop correction. When I am reading Quantum Field Theory by Mark Srednicki and Journeys Beyond the Standard Model by Pierre Ramond, I notice some ...
- 81
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
0
votes
1
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103
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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
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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
2
answers
122
views
Is there any physical reason behind the choice of Lie group in a Yang-Mills theory?
A Yang-Mills theory can be constructed for any Lie group that is compact and semisimple. The motivation behind this is discussed in this question. Is there any physical reason we choose $SU(3)$ or $U(...
- 3,350
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2
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76
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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
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93
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Standard Model irreducible representation notations
Does anyone know what the significance/meaning of the subscripts on the following notations for the irreps. in the Standard Model?
an up, down left-hand fermion (quark) pair $(u,d)_L$ is denoted: $(\...
- 11
2
votes
1
answer
78
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What kind of a space is $\mathbb{C}_{-1}$?
In the first paragraph on page 24 of this paper: https://arxiv.org/abs/0904.1556, it's written
the left-handed leptons $\nu_L$ and $e^−_L$ both have hypercharge $Y=−1$, so each one spans a copy of $\...
- 392
0
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0
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73
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Do we know a reason for why exactly $\rm U(1)$, $\rm SU(2)$ and $\rm SU(3)$? [duplicate]
I always found it a curiousity that in the symmetry groups of the known fundamental forces we find the nice arithmetic progression $1,2,3$: first there is $\DeclareMathOperator{\U}{U}\...
- 531
1
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1
answer
215
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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
0
votes
0
answers
63
views
$U(n)$ vs $SU(n)$ Symmetry and Tracelessness - Chargeless Gauge Bosons
I've recently been studying the symmetries that give rise to the bosons of the standard model. I have taught myself just enough group theory to kind of understand what $U(1)$, $SU(2)$, and $SU(3)$ ...
- 87
2
votes
1
answer
70
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Is the electroweak gauge group a semidirect product?
In the typical treatment of electroweak theory, the gauge group is $G = \mathrm{SU}(2)_I \times \mathrm{U}(1)_Y$. This group is broken by the Higgs mechanism, while the combination of generators $Q = ...
- 744
3
votes
1
answer
177
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Custodial transformation in the SM Higgs
I am reading this paper (or this link), and I'm troubled by the custodial transformation. So, I will use the notations and equation labels appearing in this paper.
If we write the Higgs field into the ...
- 1,421
1
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0
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107
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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