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Abstract: The Standard Model of particle physics may seem complicated and arbitrary,but it has hidden patterns that are revealed by the relationship between three-grand unified theories-: theories that unify forces and particles by extendingthe Standard Model symmetry group U1 x SU2 x SU3 to a larger group. Thesethree theories are Georgi and Glashow-s SU5 theory, Georgi-s theory based onthe group Spin10, and the Pati-Salam model based on the group SU2 x SU2 xSU4. In this expository account for mathematicians, we explain only theportion of these theories that involves finite-dimensional grouprepresentations. This allows us to reduce the prerequisites to a bare minimumwhile still giving a taste of the profound puzzles that physicists arestruggling to solve.

Autor: John C. Baez, John Huerta


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