PIRSA:21040005

# Can We Understand the Standard Model Using Octonions?

### APA

Baez, J. (2021). Can We Understand the Standard Model Using Octonions?. Perimeter Institute. https://pirsa.org/21040005

### MLA

Baez, John. Can We Understand the Standard Model Using Octonions?. Perimeter Institute, Apr. 12, 2021, https://pirsa.org/21040005

### BibTex

```          @misc{ pirsa_21040005,
doi = {10.48660/21040005},
url = {https://pirsa.org/21040005},
author = {Baez, John},
keywords = {Mathematical physics, Particle Physics, Quantum Fields and Strings},
language = {en},
title = {Can We Understand the Standard Model Using Octonions?},
publisher = {Perimeter Institute},
year = {2021},
month = {apr},
note = {PIRSA:21040005 see, \url{https://pirsa.org}}
}
```

John Baez University of California

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## Abstract

Dubois-Violette and Todorov have shown that the Standard Model gauge group can be constructed using the exceptional Jordan algebra, consisting of 3×3 self-adjoint matrices of octonions. After an introduction to the physics of Jordan algebras, we ponder the meaning of their construction. For example, it implies that the Standard Model gauge group consists of the symmetries of an octonionic qutrit that restrict to symmetries of an octonionic qubit and preserve all the structure arising from a choice of unit imaginary octonion. It also sheds light on why the Standard Model gauge group acts on 10d Euclidean space, or Minkowski spacetime, while preserving a 4+6 splitting.