Hilbert Book Model Project/Slide F1

hbmp	Hilbert Book Model Project	F1
	A quaternion $q$ is a combination of a scalar real part $q_r$ and an imaginary part that is represented by a three dimensional spatial vector $\overrightarrow{q}$ $q=q_r+\overrightarrow{q}$
	The quaternionic nabla is defined by $\mathrm{\nabla }=\{\frac{\partial }{\partial \tau },\frac{\partial }{\partial x},\frac{\partial }{\partial y},\frac{\partial }{\partial z}\}={\mathrm{\nabla }}_r+\overrightarrow{\mathrm{\nabla }};{\mathrm{\nabla }}_r=\frac{\partial }{\partial \tau };\overrightarrow{\mathrm{\nabla }}=\{\frac{\partial }{\partial x},\frac{\partial }{\partial y},\frac{\partial }{\partial z}\}$
	The quaternionic Template:Font splits in five terms that conform to the quaternionic multiplication rule
	$c=c_r+\overrightarrow{c}=ab=(a_r+\overrightarrow{a})(b_r+\overrightarrow{b})=a_r{b}_r-⟨\overrightarrow{a},\overrightarrow{b}⟩+a_r\overrightarrow{b}+\overrightarrow{a}{b}_r\pm \overrightarrow{a}\times \overrightarrow{b}$ The $\pm$ indicates that right handed quaternions and left handed quaternions exist
	$\phi ={\phi }_r+\overrightarrow{\phi }=\mathrm{\nabla }\psi =({\mathrm{\nabla }}_r+\overrightarrow{\mathrm{\nabla }})({\psi }_r+\overrightarrow{\psi })={\mathrm{\nabla }}_r{\psi }_r-⟨\overrightarrow{\mathrm{\nabla }},\overrightarrow{\psi }⟩+{\mathrm{\nabla }}_r\overrightarrow{\psi }+\overrightarrow{\mathrm{\nabla }}{\psi }_r\pm \overrightarrow{\mathrm{\nabla }}\times \overrightarrow{\psi }$
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