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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) $×$ SU(2) $×$ 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) $×$ SU(2) $×$ SU(4) group.
##### MSC:
 81V22 Unified theories of elementary particles 81R05 Representations of finite-dimensional groups and algebras in quantum theory 20C35 Applications of group representations to physics 81-02 Research monographs (quantum theory) 22E70 Applications of Lie groups to physics; explicit representations 81R40 Symmetry breaking (quantum theory) 81V05 Strong interaction, including quantum chromodynamics