A topological model of composite preons from the minimal ideals of two Clifford algebras

Abstract

We demonstrate a direct correspondence between the basis states of the minimal ideals of the complex Clifford algebras $\mathbb{C}\ell (6)$ and $\mathbb{C}\ell (4)$, shown earlier to transform as a single generation of leptons and quarks under the Standard Model's unbroken $SU(3{)}_c\times U(1{)}_{em}$ and $SU(2{)}_L$ gauge symmetries respectively, and a simple topologically-based toy model in which leptons, quarks, and gauge bosons are represented as elements of the braid group $B_3$. It was previously shown that mapping the basis states of the minimal left ideals of $\mathbb{C}\ell (6)$ to specific braids replicates precisely the simple topological structure describing electrocolor symmetries in an existing topological preon model. This paper extends these results to incorporate the chiral weak symmetry by including a $\mathbb{C}\ell (4)$ algebra, and identifying the basis states of the minimal right ideals with simple braids. The braids corresponding to the charged vector bosons are determined, and it is demonstrated that weak interactions can be described via the composition of braids.

11 pages

References in corpus (7)

• Quantum gravity and the standard model
• A topological model of composite preons
• Standard model physics from an algebra?
• Three fermion generations with two unbroken gauge symmetries from the complex sedenions
• The Standard Model particle content with complete gauge symmetries from the minimal ideals of two Clifford algebras
• Braided fermions from Hurwitz algebras
• Quantum groups and braid groups as fundamental symmetries

Cited by in corpus (5)

• The Standard Model particle content with complete gauge symmetries from the minimal ideals of two Clifford algebras
• Three generations of colored fermions with $S_3$ family symmetry from Cayley-Dickson sedenions
• Algebraic realisation of three fermion generations with $S_3$ family and unbroken gauge symmetry from $\mathbb{C}\ell (8)$
• Braided matter interactions in quantum gravity via 1-handle attachment
• Preons, Braid Topology, and Representations of Fundamental Particles