Quarks and leptons as ideals of the Clifford algebra CL(6) (Video 11/14)

Video 11 of 14

* It should be noted that CL(6) has just a single 8C dimensional irreducible representation under the left action. The two ideals presented here may be combined via right multiplication of the algebra on itself, as described in the next video.

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

[Zeke-Z]

Made it this I've never felt so compelled by math before. Underlying mathematical structures, how fascinating! You should teach this as an actual course online, the flow is great and I don't feel like a complete lizard trying to follow it! Thank you for this!

"That is until you divide by 3." **drops the mic**

[Tagnar]

I have absolutely no idea what any of this is and I love it.

[roberthayter]

Wow. Elsewhere people seem to think the three generations are a mystery. Here the three generations are explained. Breathtaking.

[shayangfkk]

Wow, Just amazing, many people who study physics need to watch this course for a deeper understanding and roots of all Standard model .

[MichaelHolroyd]

Should have used a hand held mic so you could drop it.

[majikwon]

Thank you, Dr Furey. This is a very interesting perspective on the necessity of the Standard Model. However, I don't have any experience working with Clifford algebras and left ideals, etc. And everything I find on the web seem like graduate level math. Not having been in school for a while, I could use a premier that takes me through all these concepts with a change to get some practice with exercises. Can you recommend any texts? Thanks.

[reklamukibiras]

Brilliant findings, but what bothers me is that particles and antiparticles are mixed up between the tables - every odd in Q and every even in -Q. Yes, they are sorted by charge, but not by natural abundance. It feels like (-1)^n is missing hidden somewhere, maybe in number operator N, or maybe someplace else. It could give tables sorted by matter / antimatter principle, and charge would come second. Not sure if it would affect complex quaternions, it might change order of spins though (as in video #6). If (-1)^n is not in number operator N, then it is still an open question to find a relation how and why matter jumps from one table to another with every charge quantum

[trippivey]

So many symbols and words i dont understand. Im completley lost but i cant quit watching.

[wellingtontravassos]

Amazing...i'm really excited about this new theory...greetingsss from brazillll!!!

[TheWyrdSmythe]

Holy Canole, I actually followed most of that, at least at a high level. Those triplets... the color charge of the quarks? And what about the other two generations of particles?

I assume mass remains a measured constant?

[kirchdubl]

this must be some sort of conspiracy, you cannot deduce fundamental physics by pure math, but still cannot figure out where is the catch, this really make sense

[Evan]

Is associativity needed because otherwise one can't find a unique projector that includes all the ladder operators?

[rrrbb]

is there a reason to use change units such that electron is -1? would more obvious patterns arise if we multiply all changes times -3 vs their current unit? (same issue for spin?) this really looks like a more complicated notation for basic Geometric Algebra to me.

[bouhschnou]

is the spin stored in a1a2a3? (a sign in the expresion of ai?)

[nolan]

Square instead of dividing by 3 and looks bit like 1/ 1st Gen mass.

[flamephlegm]

How would you explain all of this to a five year old?