Arcadian Functor

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Marni D. Sheppeard

Sunday, May 20, 2007

M Theory Lesson 57

Recall that the Bilson-Thompson diagrams for left and right handed electrons are formed with three strands, each with a full negative twist representing a one third charge. Ignoring the twists, the simplest braid composition of the form $e_L e_R e_L$ looks like this: This knot is called a $6_3$ knot, according to the amazing online knot atlas, which lists the polynomial invariants for this knot. For example, the Jones polynomial takes the form

$-q^3 + 2 q^2 -2q + 3 -2 q^{-1} + 2 q^{-2} - q^{-3}$

Since all negative twists add up on going around the knot, there is a total ninefold twist. There is now a button to the knot atlas on the sidebar.

3 Comments:

Blogger Doug said...

Hi Kea,
RE: Bilson-Thompson diagrams for left and right handed electrons.

To satisfy QCD and make a more powerful presentation perhaps the stings need to be of different colors?

your reference and:
http://webphysics.davidson.edu/mjb/qcd.html

May 21, 2007 1:05 AM  
Blogger kneemo said...

Kea

How could one represent e/5 charge using Bilson-Thompson-like diagrams?

May 21, 2007 9:27 AM  
Blogger Kea said...

How could one represent e/5 charge?

Wouldn't we need 5 strands (elements of B5) for that? Then a full twist on any strand would count for e/5. Hmm. The other possibility is Iteration: thinking of this 3 piece composition as giving charge 1 strands, then 5 finer strands internal to a single strand could count twists as e/5.

May 21, 2007 9:36 AM  

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