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AuthorDixon, Geoffrey M. author
TitleDivision Algebras [electronic resource] : Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics / by Geoffrey M. Dixon
ImprintBoston, MA : Springer US : Imprint: Springer, 1994
Connect tohttp://dx.doi.org/10.1007/978-1-4757-2315-1
Descript X, 238 p. online resource

SUMMARY

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 renยญ 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


CONTENT

I Underpinnings -- II Division Algebras Alone -- III Tensor Algebras -- IV Connecting to Physics -- V Spontaneous Symmetry Breaking -- VI 10 Dimensions -- VII Doorways -- VIII Corridors


Mathematics Matrix theory Algebra Nonassociative rings Rings (Algebra) Applied mathematics Engineering mathematics Nuclear physics Heavy ions Hadrons Mathematics Applications of Mathematics Non-associative Rings and Algebras Nuclear Physics Heavy Ions Hadrons Linear and Multilinear Algebras Matrix Theory



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