Construction and characterization of representations of su(7) for gut model builders

Daniel Jones; Jeffery A. Secrest

doi:10.3390/sym13061044

Construction and characterization of representations of su(7) for gut model builders

Daniel Jones, Jeffery A. Secrest

Biochemistry, Chemistry, & Physics

Georgia Southern University

Research output: Contribution to journal › Article › peer-review

Abstract

The natural extension to the SU(5) Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the SU(7) symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the SU(7) algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the SU(7) Lie group to supersymmetric grand unification as well as applications are discussed.

Original language	English
Article number	1044
Journal	Symmetry
Volume	13
Issue number	6
DOIs	https://doi.org/10.3390/sym13061044
State	Published - Jun 2021

Keywords

Gauge group
Gauge symmetry breaking
Grand unified theories
GUT
Leptons
Lie algebra
Quarks

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10.3390/sym13061044

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abstract = "The natural extension to the SU(5) Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the SU(7) symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the SU(7) algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the SU(7) Lie group to supersymmetric grand unification as well as applications are discussed.",

keywords = "Gauge group, Gauge symmetry breaking, Grand unified theories, GUT, Leptons, Lie algebra, Quarks",

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AB - The natural extension to the SU(5) Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the SU(7) symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the SU(7) algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the SU(7) Lie group to supersymmetric grand unification as well as applications are discussed.

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KW - Gauge symmetry breaking

KW - Grand unified theories

KW - GUT

KW - Leptons

KW - Lie algebra

KW - Quarks

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Construction and characterization of representations of su(7) for gut model builders

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Keywords

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