How the complex quaternions give each of the Lorentz reps of the standard model (Video 7/14)

Video 7 of 14

Series: Division algebras and the standard model

Some short videos filmed by Vincent Lavigne

Seminar by C. Furey,
Walter Grant Scott Research Fellow in Physics
Trinity Hall, University of Cambridge

[gnmn]

This should be taught in all second year particle theory courses, imo

[machinelearning]

Do you think that Clifford algebra is intrinsically non local in the kind of geometry which emerges from two entangled Majorana type spinors? Which are - from a mathematical point of view - the meaning and the implications of non local causality in QM?

[bezbezzebbyson]

I have a question. How does this algebraic formulation of physics eliminates the need for geometry? I don't know much but so far it sounds that you could describe the standard model on a R × C × H × O fiber bundle over spacetime. We still need fields right?

[jackpitts]

Perhaps I've not found the first two videos in this series, but why do you call them "complex quaternions" rather than "octonions"?

[bba]

I use pretty much the same method clarify my quotes for my 1 man and a truck furniture removals.

[vaidphysics]

A beautiful construction! But if you want a theory with all the components: spinors, 4 vectors, scalars and tensors; then you would need (at least) three copies of C x H, right?

[TheWyrdSmythe]

Seeing dimly through a dark glass. Dang it, I wish I had a better grasp, but I keep reaching. I do at least recognize something like F’ = LF~L from my exploration of rotation quaternions. Weird how that works.

[paulmccaffrey]

Interesting. Now, can this be applied to discrete, iterative functions? That's what I'm trying to figure out now. Time and space are clearly discrete.

[OnlyPenguian]

I must admit to being a bit lost here. What, exactly, does "transforms like this" mean? What is the transformation? Is it defined in the thesis? Sorry for all the questions. I am just trying to understand all the jargon, and the motivation for it.

[fabriziocaragiulo]

"transforms like this" under what?

[machinelearning]

Give me 4 numbers ( 🔠)
and I'll raise the world (🌐)

(🔠) quaternion algebra
(🌐) the standard model

With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.
Attributed to von Neumann by Enrico Fermi, as quoted by Freeman Dyson in "A meeting with Enrico Fermi"