Center for Theoretical Physics of the Universe (CTPU-PTC)

Division algebras and the standard model

by Dr Cohl Furey


We explain how an unexpected algebraic structure, the division algebras, can be seen to underlie a generation of quarks and leptons.  From this new vantage point, electrons and quarks are simply excitations from the neutrino, which (formally) plays the role of a vacuum state.

Using the ladder operators which exist within the system, we then build a number operator in the usual way.  It turns out that this number operator, divided by 3, mirrors the behaviour of electric charge.  As a result, we see that electric charge is quantized because number operators can only take on integer values.

Finally, we show that symmetries of these ladder operators result uniquely in the nine generators of SU(3)c and U(1)
em. This gives a direct route to the two unbroken gauge symmetries of the standard model.