# Contents

## Idea

The standard model of particle physics asserts that the fundamental quantum physical fields and particles are modeled as sections of and connections on a vector bundle that is associated to a $G$-principal bundle, where the group $G$ is $\mathrm{SU}\left(3\right)×\mathrm{SU}\left(2\right)×U\left(1\right)$ (or perhaps a quotient of this by ${Z}_{6}$) and where the representation of $G$ used to form the associated vector bundle looks fairly ad hoc on first sight.

A grand unified theory in this context is an attempt to realize the standard model as sitting inside a conceptually simpler model, in particular one for which the structure group – the gauge group – is a bigger but simpler group $\stackrel{^}{G}$, preferably a simple group, which contains $G$ as a subgroup.

## References

A good introduction to GUTs for mathematicians is

Blog discussion of this is at

Revised on August 21, 2012 17:22:09 by Urs Schreiber (82.113.99.27)