Group Geometric Algebra and the Standard Model

• 作者: Carl Brannen​
• 来源期刊: 现代物理(英文)
• 学科: 数学
• 关键词: Weyl Equation Dark Matter Standard Model
• 年，卷（期）: 2020,（8）
• 页码范围: 1193-1214
• 页数: 22页
• 分类号: O17

摘要

We show how to generalize the Weyl equation to include the Standard Model fermions and a dark matter fermion. The 2 × 2 complex matrices are a matrix ring <em>R</em>. A finite group <em>G</em> can be used to define a group algebra <em>G[R]</em> which is a generalization of the ring. For a group of size <em>N</em>, this defines <em>N</em> Weyl equations coupled by the group operation. We use the group character table to uncouple the equations by diagonalizing the group algebra. Using the full octahedral point symmetry group for <em>G</em>, our uncoupled Weyl equations have the symmetry of the Standard Model fermions plus a dark matter particle. We describe the symmetry properties of dark matter.