The Algebra of Grand Unified Theories

Details The Algebra of Grand Unified Theories The Algebra of Grand Unified Theories

2009-04-09

arxiv.org/abs/0904.1556v2

Bull.Am.Math.Soc.47:483-552,2010

Physics

High Energy Physics

High Energy Physics - Theory

73 pages, 20 ps figures

Scientific paper

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.

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