## 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?

http://webphysics.davidson.edu/mjb/qcd.html

2. 2

### kneemo said,

Kea

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.