The Algebra of Grand Unified Theories
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 PatiSalam 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 finitedimensional 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2009
 arXiv:
 arXiv:0904.1556
 Bibcode:
 2009arXiv0904.1556B
 Keywords:

 High Energy Physics  Theory;
 High Energy Physics  Phenomenology;
 Mathematics  Representation Theory
 EPrint:
 73 pages, 20 ps figures