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About Group Representations in Grand Unified Theories
Author(s) -
Grech Dariusz K.
Publication year - 1985
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190330502
Subject(s) - unification , grand unified theory , group (periodic table) , mathematics , representation (politics) , scheme (mathematics) , unified field theory , degrees of freedom (physics and chemistry) , group representation , pure mathematics , algebra over a field , theoretical physics , computer science , physics , mathematical analysis , mathematical physics , supersymmetry , quantum mechanics , politics , political science , law , programming language
Abstract The main purpose of this article is to systematize group theory methods in Grand Unified Theories (GUTs). An exact representation structure for all admissible groups that unify elementary forces is analysed. The implications of requirements asymptotic freedom for standard SU (3) c ⊗ SU (2) L ⊗ U (1) y model is investigated in detail. It is shown how restrictive are such assumptions in unified model building. As a result the maximal number of families is five independently on the kind of considered model. In several cases this number is even smaller. The maximal horizontal structure of interactions which is possible to embed into unification scheme is also discussed for all admissible models. The number of superheavy particles is evaluated in different unifying schemes.