## The algebra of grand unified theories

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- by John Baez and John Huerta PDF
- Bull. Amer. Math. Soc.
**47**(2010), 483-552

## Abstract:

The Standard Model is the best tested and most widely accepted theory of elementary particles we have today. It 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 extending the Standard Model symmetry group $\mathrm {U}(1) \times \mathrm {SU}(2) \times \mathrm {SU}(3)$ to a larger group. These three are Georgi and Glashow’s $\mathrm {SU}(5)$ theory, Georgi’s theory based on the group $\textrm {Spin}(10)$, and the Pati–Salam model based on the group $\mathrm {SU}(2) \times \mathrm {SU}(2) \times \mathrm {SU}(4)$. In this expository account for mathematicians, we explain only the portion of these theories that involves finite-dimensional group representations. This allows us to reduce the prerequisites to a bare minimum while still giving a taste of the profound puzzles that physicists are struggling to solve.## References

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## Additional Information

**John Baez**- Affiliation: Department of Mathematics, University of California, Riverside, California 92521
- Email: baez@math.ucr.edu
**John Huerta**- Affiliation: Department of Mathematics, University of California, Riverside, California 92521
- Email: huerta@math.ucr.edu
- Received by editor(s): May 8, 2009
- Received by editor(s) in revised form: October 16, 2009
- Published electronically: March 11, 2010
- Additional Notes: This research was supported by a grant from the Foundational Questions Institute.
- © Copyright 2010 John C. Baez and John Huerta
- Journal: Bull. Amer. Math. Soc.
**47**(2010), 483-552 - MSC (2000): Primary 20C35, 81R05; Secondary 81-02
- DOI: https://doi.org/10.1090/S0273-0979-10-01294-2
- MathSciNet review: 2651086