Charge quantization from a number operator

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.Comment: 6 pages, 2 figure

A demonstration that electroweak theory can violate parity automatically (leptonic case)

“…5,22,33,49 In particular, we continue to work towards understanding where this specific Clifford algebraic structure comes from. Of the infinite number of Clifford algebras available, why would nature choose Cl(4)?…”

“…In short, the model yields quite efficiently the basic electroweak behaviour for one generation of standard model leptons, together with a right-handed neutrino. This result may be useful for authors with an interest in left-right asymmetry models, 6-21 existing Clifford algebraic particle models, [23][24][25][26][27][28][29][30][31][32][33][34] beyond-the-standardmodel proposals, [35][36][37] and noncommutative geometry.…”

Unification mechanism for gauge and spacetime symmetries

“…. × u(1), and the Levi factor being extended by the Lie algebra of a compact gauge (internal) group g: (12) Here, the arrow diagram explicitly shows that the glueing of the compact gauge (internal) symmetries and the Lorentz symmetries are possible due to their common adjoint Lie group action on some subspace (q ext ) of the radical. In that sense, the unification mechanism Eq.…”

The Standard Model Algebra - a summary

“…This is essential to account for the fact that in each minimal left ideal actually live two particles, whose charge differs exactly by this value. A proof that unitary spin transformations preserving a Witt decomposition in C 6 give these symmetries, and a set of generators constructed from the q j and q † j but equivalent to (36), was given by Furey [9]. Based on the algebra C 7 , [8] proposed generators of SU(3) c are equivalent to (36) via to the isomorphisms C 7 ∼ = M C (8) ∼ = C 6 .…”

“…Furey uses the Witt decomposition for C 6 in a model based on octonions [9,10], to represent colors and charges of up-and down-type particles by q † K qq † and q K q † q, on the minimal left ideals C 6 qq † and C 6 q † q. They are united into a single irreducible representation of C 6 ⊗ C C 2 obtained by using the octonion algebra.…”