# End of Chapter 3

NDER    ONSTRUCTION

## Conclusions

3.1) From a gluon the color k (e.g. color k) has to be assigned to the coupling, in fact one k at both ends of the gluon. A gluon maybe rather is a line segment than a point particle.

3.2) When particles couple, the colors (quaternion units) of the particles must be multiplied. When particles stay together but do not merge, their colors sum up.

3.3) The physical interpretation of multiplication order is: start multiplying with this, a little later with that and at last with this.

3.4) Quarks have color and antiquarks have anticolor.

3.5) In QCD a color (of a quark) is multiplied by a Gell-Mann matrix (a gluon) in order to yield another color (of the quark). In QQD the gluon is one single color too, just like the quarks. In QQD a color times a color always yields a color again (a quaternion unit times a quaternion unit always yields a quaternion unit).

3.6) A Gell-Mann matrix (a gluon) is a kind of Pauli matrix. In QQD each gluon color is the product of TWO Pauli matrices. Except for -1 that needs 4 or 6 Pauli matrices.

3.7) IF the Pauli matrices that compose a quaternion unit can be orthogonal THEN quaternion 1ijk space can be SU(2).

3.8) Representing quaternions by real 4 x 4 matrices indicate that quaternions are SO(4).

## Discussion

3.1) Do 3 gluons indeed merge easier than 2 gluons do? (page 7 of QCD, no part of the TONE storyline)

3.2) In 2014 and 2016 I contacted prof. Piet Mulders from VU University, Amsterdam, and I found him willing to read my proposal to a paper about Gluons as Quaternions that followed mainly the scheme of paragraph Gell-Mann matrices at page 9 of QQD.

Prof. Mulder replied that the matrices I proposed indeed are symmetries, but they don't obey the commutation relation [A,B] = C no more, where C is a Lie-algebra. The group decays in a number of subsets that cannot represent all of QCD no more and you have to perform quite some acrobatics to repair this. This doesn't make things simpler nor easier, he said.

My proposition was (and still is) to replace the classic gluon with 3 entries for color by a 2x2 matrix for each color, 2 entries per gluon that is. With quaternion units this can be done. I am not familiar with Lie-algebra's so I cannot judge the commentary. I decided to continue with my findings so far.

3.3) If the Pauli matrices that compose a quaternion unit are orthogonal, do they exclude each other then? And what does that mean?

3.4) Discussion points about dark multiplication rules between two opposite colors like e.g. i and -j, are removed to paragraph Two gluons of opposite sign do not react at page 3 of QG.

3.5) Is the black glueball candidate for Dark Matter? Do primordial black glueballs have no choice than to roam around? What is the mass of the black gluon? More about the black glueball at page 41 in the next chapter of TONE.