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**The algebra of grand unified theories.**
*(English)*
Zbl 1196.81252

This is the paper that is treated as a gentle introduction for mathematicians to the algebra of the Standard Model of particle physics which is actually the best tested and the most widely accepted theory of describing all the particles and all the forces of nature, except gravity. Three grand unified theories which unify particles and forces beyond the Standard Model via extending the latter gauge group U(1) \(\times\) SU(2) \(\times\) SU(3) are thoroughly reviewed. These are Georgi-Glashow’s SU(5) theory, Georgi’s theory based on the Spin(10) or SO(10) group, and the Pati-Salam model based on the SU(2) \(\times\) SU(2) \(\times\) SU(4) group.

Reviewer: Eugene Kryachko (Liège)

### MSC:

81V22 | Unified quantum theories |

81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |

20C35 | Applications of group representations to physics and other areas of science |

81-02 | Research exposition (monographs, survey articles) pertaining to quantum theory |

22E70 | Applications of Lie groups to the sciences; explicit representations |

81R40 | Symmetry breaking in quantum theory |

81V05 | Strong interaction, including quantum chromodynamics |

### Keywords:

standard model; grand unified theory; symmetry breaking; unification; SU(5); Spin(10); gauge group; isospin; intertwining operator; Gell-Mann-Nishijima formula; hypercharge; fundamental fermions; flavor; quark; color; gauge bosons; Dirac spinor; Pati-Salam model
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\textit{J. Baez} and \textit{J. Huerta}, Bull. Am. Math. Soc., New Ser. 47, No. 3, 483--552 (2010; Zbl 1196.81252)

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