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| | Hola! I am Dalton. Acting should be a thing that Now i'm totally addicted to. My carry is now in Vermont and I don't design on changing it. I am a cashier. I'm not awesome at webdesign but you may be want to check my website: http://circuspartypanama.com<br><br>Also visit my homepage [http://circuspartypanama.com clash of clans hack no survey no download] |
| {{Technical|section=|date=July 2009}}
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| {{Expert-subject|Physics|date=July 2009}}
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| {{Unreferenced|date=July 2009}}
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| In [[physics]], the '''trinification model''' is a [[Grand unification theory|GUT]] theory.
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| It states that the [[gauge group]] is either
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| :<math>SU(3)_C\times SU(3)_L\times SU(3)_R</math>
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| or
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| :<math>[SU(3)_C\times SU(3)_L\times SU(3)_R]/\mathbb{Z}_3</math>;
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| and that the fermions form three families, each consisting of the [[Representations of Lie groups/algebras|representations]] :<math>(3,\bar{3},1)</math>, <math>(\bar{3},1,3)</math> and :<math>(1,3,\bar{3})</math>.
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| This includes the right-handed neutrino, which can account for observed neutrino masses (but has not yet been proved to exist). See [[neutrino oscillation]]s.
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| There is also a <math>(1,3,\bar{3})</math> and maybe also a <math>(1,\bar{3},3)</math> [[scalar field]] called the [[Higgs field]] which acquires a VEV. This results in a [[spontaneous symmetry breaking]] from
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| :<math>SU(3)_L\times SU(3)_R</math> to <math>[SU(2)\times U(1)]/\mathbb{Z}_2</math>
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| and also,
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| :<math>(3,\bar{3},1)\rightarrow(3,2)_{\frac{1}{6}}\oplus(3,1)_{-\frac{1}{3}}</math>,
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| :<math>(\bar{3},1,3)\rightarrow2\,(\bar{3},1)_{\frac{1}{3}}\oplus(\bar{3},1)_{-\frac{2}{3}}</math>,
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| :<math>(1,3,\bar{3})\rightarrow2\,(1,2)_{-\frac{1}{2}}\oplus(1,2)_{\frac{1}{2}}\oplus2\,(1,1)_0\oplus(1,1)_1</math>,
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| :<math>(8,1,1)\rightarrow(8,1)_0</math>,
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| :<math>(1,8,1)\rightarrow(1,3)_0\oplus(1,2)_{\frac{1}{2}}\oplus(1,2)_{-\frac{1}{2}}\oplus(1,1)_0</math>,
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| :<math>(1,1,8)\rightarrow 4\,(1,1)_0\oplus 2\,(1,1)_1\oplus 2\,(1,1)_{-1}</math>.
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| See [[restricted representation]].
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| Note that there are '''two''' [[Majorana spinor|Majorana]] neutrinos per generation (which is consistent with [[neutrino oscillation]]s). Also, a copy of
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| <math>(3,1)_{-\frac{1}{3}}</math> and <math>(\bar{3},1)_{\frac{1}{3}}</math>
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| as well as
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| <math>(1,2)_{\frac{1}{2}}</math> and <math>(1,2)_{-\frac{1}{2}}</math>
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| per generation decouple at the GUT breaking scale due to the couplings
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| <math>(1,3,\bar{3})_H(3,\bar{3},1)(\bar{3},1,3)</math>
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| and
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| <math>(1,3,\bar{3})_H(1,3,\bar{3})(1,3,\bar{3})</math>.
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| Note that calling the [[Representations of Lie groups/algebras|representations]] things like <math>(3,\bar{3},1)</math> and (8,1,1) is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by [[Young tableau]]x or [[Dynkin diagram]]s with numbers on their vertices, but still, it is standard among GUT theorists.
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| Since the [[homotopy group]]
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| <math>\pi_2\left(\frac{SU(3)\times SU(3)}{[SU(2)\times U(1)]/\mathbb{Z}_2}\right)=\mathbb{Z}</math>,
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| this model predicts [[Magnetic monopole|monopoles]]. See [['t Hooft-Polyakov monopole]].
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| This model is suggested by [[Sheldon Lee Glashow]], [[Howard Georgi]] and [[Alvaro de Rujula]], in 1984. This is one of the [[maximal subalgebra]] of E6, whose matter representation 27 has exactly the same representation as above.
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| ==References==
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| {{Reflist}}
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| [[Category:Particle physics]]
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Hola! I am Dalton. Acting should be a thing that Now i'm totally addicted to. My carry is now in Vermont and I don't design on changing it. I am a cashier. I'm not awesome at webdesign but you may be want to check my website: http://circuspartypanama.com
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