# Hilbert Book Model Project/Slide S8

hbmp Hilbert Book Model Project S8

In the multiplication ${\displaystyle {\color {white}c=ab/a}}$, the imaginary part of ${\displaystyle {\color {white}b}}$ that is perpendicular to the imaginary part of ${\displaystyle {\color {white}a}}$
is rotated over an angle that is twice the complex phase ${\displaystyle {\color {white}a_{\varphi }}}$ of ${\displaystyle {\color {white}a}}$

This fact means that if ${\displaystyle {\color {white}a_{\varphi }=\pi /4}}$, then the rotation ${\displaystyle {\color {white}a\,b/a}}$ shifts ${\displaystyle {\color {white}b_{\perp }}}$to another dimension

This fact puts quaternions for which the size ${\displaystyle {\color {white}|a_{r}|}}$ of the real part equals the size ${\displaystyle {\color {white}|{\vec {a}}|}}$ of the imaginary part
in a special category.

They can switch states of quaternionic tri-state systems.
In addition, they can switch the color charge of quarks.

This means that such enveloping pairs behave as gluons

This fact raises the suggestion that the these gluons play a role in the color confinement,
which prevents quarks from binding or interacting before the gluons shift them to neutral color charge

If color shifting precedes spectral binding, then the resulting binding appears stronger

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