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- Title
Sedenion Algebra Model as an Extension of the Standard Model and Its Link to SU(5).
- Authors
Tang, Qiang; Tang, Jau
- Abstract
In the Standard Model, ad hoc hypotheses assume the existence of three generations of point-like leptons and quarks, which possess a point-like structure and follow the Dirac equation involving four anti-commutative matrices. In this work, we consider the sedenion hypercomplex algebra as an extension of the Standard Model and show its close link to SU(5), which is the underlying symmetry group for the grand unification theory (GUT). We first consider the direct-product quaternion model and the eight-element octonion algebra model. We show that neither the associative quaternion model nor the non-associative octonion model could generate three fermion generations. Instead, we show that the sedenion model, which contains three octonion sub-algebras, leads naturally to precisely three fermion generations. Moreover, we demonstrate the use of basis sedenion operators to construct twenty-four 5 × 5 generalized lambda matrices representing SU(5) generators, in analogy to the use of octonion basis operators to generate Gell-Mann's eight 3 × 3 lambda-matrix generators for SU(3). Thus, we provide a link between the sedenion algebra and Georgi and Glashow's SU(5) GUT model that unifies the electroweak and strong interactions for the Standard Model's elementary particles, which obey SU(3) ⊗ SU(2) ⊗ U(1) symmetry.
- Subjects
STANDARD model (Nuclear physics); ALGEBRA; PARTICLES (Nuclear physics); DIRAC equation; ELECTROWEAK interactions; CAYLEY numbers (Algebra)
- Publication
Symmetry (20738994), 2024, Vol 16, Issue 5, p626
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym16050626