An Algebraic Roadmap of Particle Theories, Part II: Theoretical checkpoints

Abstract

An optimal algebraic model of particle physics has a number of checkpoints to pass. As a minimum, models should $\langle 1 \rangle$ conform to the Coleman-Mandula theorem (or establish a loophole), $\langle 2 \rangle$ evade familiar fermion doubling problems, $\langle 3 \rangle$ naturally explain the Standard Model's chirality, $\langle 4 \rangle$ exclude B-L gauge symmetry at low energy, and $\langle 5 \rangle$ explain the existence of three generations. We demonstrate how the model introduced in [1] passes checkpoints $\langle 1 \rangle, \langle 2 \rangle, \langle 3 \rangle, \langle 4 \rangle$, and has yet to cross $\langle 5 \rangle$. We close by elucidating an unexpected appearance of spacetime symmetries.