Division Algebras

Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics

  • Geoffrey M. Dixon

Part of the Mathematics and Its Applications book series (MAIA, volume 290)

Table of contents

  1. Front Matter
    Pages i-x
  2. Geoffrey M. Dixon
    Pages 1-30
  3. Geoffrey M. Dixon
    Pages 31-57
  4. Geoffrey M. Dixon
    Pages 59-81
  5. Geoffrey M. Dixon
    Pages 83-108
  6. Geoffrey M. Dixon
    Pages 109-115
  7. Geoffrey M. Dixon
    Pages 117-139
  8. Geoffrey M. Dixon
    Pages 141-190
  9. Geoffrey M. Dixon
    Pages 191-216
  10. Back Matter
    Pages 217-238

About this book


I don't know who Gigerenzer is, but he wrote something very clever that I saw quoted in a popular glossy magazine: "Evolution has tuned the way we think to frequencies of co-occurances, as with the hunter who remembers the area where he has had the most success killing game." This sanguine thought explains my obsession with the division algebras. Every effort I have ever made to connect them to physics - to the design of reality - has succeeded, with my expectations often surpassed. Doubtless this strong statement is colored by a selective memory, but the kind of game I sought, and still seek, seems to frowst about this particular watering hole in droves. I settled down there some years ago and have never feIt like Ieaving. This book is about the beasts I selected for attention (if you will, to ren­ der this metaphor politically correct, let's say I was a nature photographer), and the kind of tools I had to develop to get the kind of shots Iwanted (the tools that I found there were for my taste overly abstract and theoretical). Half of thisbook is about these tools, and some applications thereof that should demonstrate their power. The rest is devoted to a demonstration of the intimate connection between the mathematics of the division algebras and the Standard Model of quarks and leptons with U(l) x SU(2) x SU(3) gauge fields, and the connection of this model to lO-dimensional spacetime implied by the mathematics.


Mathematica algebra energy lepton lie group physics quark standard model symmetry

Authors and affiliations

  • Geoffrey M. Dixon
    • 1
  1. 1.Brandeis UniversityUSA

Bibliographic information