Charge quantization from a number operator

TL;DR

This paper demonstrates that electric charge quantization naturally emerges from the algebraic structure of ladder operators and division algebras, linking fundamental particles to gauge symmetries in the standard model.

Contribution

It introduces a novel algebraic framework using division algebras and ladder operators to derive charge quantization and gauge symmetries of the standard model.

Findings

Charge quantization arises from the properties of a constructed number operator.

The algebraic structure yields the nine generators of SU(3)_c and U(1)_em.

Electrons and quarks are modeled as excitations from a neutrino vacuum state.

Abstract

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 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 a simple hermitian form, built from these ladder operators, results 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.