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arXiv:0904.1556hep-th

The Algebra of Grand Unified Theories

John C. Baez, John Huerta

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 extending the Standard Model symmetry group U(1) x SU(2) x SU(3) to a larger group. These three theories are Georgi and Glashow's SU(5) theory, Georgi's theory based on the group Spin(10), and the Pati-Salam model based on the group SU(2) x SU(2) x 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.

arXiv comments
73 pages, 20 ps figures
Journal reference
Bull.Am.Math.Soc.47:483-552,2010
DOI
Subjects
hep-thHigh Energy Physics, Theory hep-phHigh Energy Physics, Phenomenology math.RTRepresentation Theory

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  1. A ‘Useless’ Perspective That Transformed Mathematics 1 comment

    • Representation theory, the subject of the submitted article, is also at the core of our understanding of the particle zoo in physics. A tutorial aimed at mathematicians is here: John Baez, John Huerta. The Algebra of Grand Unified Theories. https://arxiv.org/abs/0904.1556

      IngoBlechschmidView on HNParent context

  2. What is it like to understand advanced mathematics? 1 comment

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