Henrik Jansson: The 28-fold Way: Electroweak classification and interaction

Abstract: After giving an overview of Lie algebras and the Standard Model of particle physics, we introduce four fundamental quantum numbers based on the D4 root system, giving a unified description of quarks and leptons. These numbers will make it possible to define electric charge in a simple way. By postulating a fundamental symmetry given by the binary tetrahedral group acting on this root system, we can easily prove conservation of electric charge. Also, possible electroweak interactions are given by a simple rule where the 24-cell acts on itself by quaternion multiplication. The three generations of fermions in the Standard Model are hereby identified with the three imaginary dimensions of the quaternions.