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 Responses so far »

  1. 1

    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:

  2. 2

    kneemo said,


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

  3. 3

    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.

Comment RSS · TrackBack URI

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: