Symmetry model E9CSaffine Group E9 and symmetries of its Coxeterelement
Why do we consider the E9 group (more specifically
the Coxeter element of this group)?
1) E9 is an affine group and thus has something to do with extension.
2) The extension is flat as the universe.
3) The key Coxeter element of the group produces symmetries involving our current standard model.
Derivative of the symmetries of E9CS from the invariants of the Coxeter elements E9:
The Coxeter element is the product of the generating reflections of E9.
The Coxeterpolynom is the
characteristic polynomial of Coxeter elements and
has the form:
What bring us the additional symmetries?
(1) These have the potential to describe new particles.
(2) These have the potential to describe the space and time.(3) These have the potential to describe gravity.
Light and gravitation just like photon and graviton have something in common.
Both are massless and propagate with the speed of light.
We know that light by the symmetry breaking 1: SU(2)xU (1)--> U(1) is described as a mixture.
So light is a part of the electro-weak interactions.
we consider analog gravity as a result of a further symmetry breaking
Symmetry breaking 2: U(1) x U(1) --> U(1)
Our extended standard model allows us this.
We will now like to
assign our relevant SU(n)'s to algebras division (real numbers,
complex numbers, ...).
This 4 divison algebras (real numbers, complex numbers, quaternions and octonions) develop through the doubling process
see more at https://de.wikipedia.org/wiki/Verdopplungsverfahren
Considering the dimensions of the SU(2) = 1,SU(3)= 2, SU(5) = 4 then this is double as well.
There appears to be a connection between the division algebras and the SU(n)’s (n = 2,3,5) which I hope is known in analytic geometry or another area.
I assume this connection warrants as simply as given.
Notes but no clear allocation can be found in this direction at Corinne A. Manogue and Tevian Dray, John Baez, etc.
Therefore, we rely
analogously on the Higgsfield (2
x complex = doublet)
This provides 40 degrees of
24 of which will be "spent" for our SU(5) tensor bosons for the 5th longitudinal spin degree of freedom (24 Goldstone bosons swallowed over gauge transformation) thus remain 16 left.
The S, F, R, G and H charges are the 5 charges of the SU (5) analogous to the 3 color charges of SU (3) and the 2 charges (+ .-) of SU (2).
The letters stand for S = See, F = feeling, R=smelling G = Taste and H = Hear
Calling therefore the charges of the SU (5) sense charges.Note: These charges have (such as the color charges of quarks with color) nothing to do with the senses, but to give a name to the child for reference only.
Make the following
division for the 40 field components of the Oktoquinten field as a