TITLE:
Group Geometric Algebra and the Standard Model
AUTHORS:
Carl Brannen
KEYWORDS:
Weyl Equation, Dark Matter, Standard Model
JOURNAL NAME:
Journal of Modern Physics,
Vol.11 No.8,
August
17,
2020
ABSTRACT: 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 R. A finite group G can be used to define a group algebra G[R] which is a generalization of the ring. For a group of size N, this defines N 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 G, 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.