The Octonions

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Recorded: 10/20/2018 Released: 12/23/2018

Randy tells Jim about the octonions, a cousin to the complex numbers in eight dimensions that Cohl Furey has made some headlines with by categorizing elementary particles with them. By looking at, basically, stable sets in the octonions, she has found representations that act like the elementary particles, and found ways to characterize some of their parameters, e.g., the charge, with them.
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Notes:

1. The papers we read for this program:

• Furey, C., "Unified Theory of Ideals" Phys Rev D 86, 025024 (2012). [Free]
• Furey, C, "Three Generations, Two Unbroken Gauge Symmetries, and One Eight-Dimensional Algebra" Phys Lett B 785, 84 (2018). [Free] [Supplement]

2. Related Papers:

• Furey, C., "Standard Model Physics from an Algebra" PhD. Thesis.
• Baez, J., "The Octonions." Bull. Amer. Math. Soc. 39 145 (2002).
• The Quanta magazine article that got Randy interested.

3. Related Episodes of Physics Frontiers:

• Physics Frontiers 35: The String Theory Landscape
• Physics Frontiers 30: The Consistent Histories Interpretation of Quantum Mechanics

4. Books mentioned in this podcast:

• Crowe, Michael, A History of Vector Analysis. A little bit dry, but a third of the book is about Hamilton and the quaternions.
• Whitehead, A.N., Process and Reality. If you think you're smart, try this.
• Fano and Fano, Physics of Atoms and Molecules. Lots of perturbations. That's what I remember.

5. John Baez' webpage for all things octonion.

6. Cohl Furey's video series on the octonions and the standard model.

6. Please visit and comment on our subreddit, and if you can help us keep this going by contributing to our Patreon, we'd be grateful.

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