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.


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
Full Text: DOI arXiv


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