physicists to refer to the second quantized wavefunction $\Psi$). Following Greider[@Greider], we note that the [*metric tensor*]{} $g_{\mu\nu}$ have the diagonal values $g_{11}=g_{22}=g_{33}=-g_{44}=+1$ of the [*east coast*]{} signature $(+++-)$ if the use of the commuting $i$ is excluded. Note that this means that eq. (3.2a) and most of the following results of this paper are inaccessible if the other metric $(+++-)$ with inequivalent algebra ${\bf H}(2)$ is used, as assumed by Hestenes[@Hestenes82].

Meta-Monogenic Functions
------------------------

Real solutions (no $i$) to the [*meta-harmonic*]{} Klein-Gordon eq. (3.1) are of the form: $\eigen{\phi}({\bf x}) \sim \cos{(p_{\mu}x^{\mu})} $. Substituting this eigenfunction into eq. (3.1) gives the [*characteristic equation*]{}, $$m^2 = -p_{\mu}p^{\mu} = E^2-\| \momentum \|^2 , \eqno(3.4a)$$ known in this case as the [*Einstein relation*]{} between mass $m$, energy $E$ and vector momentum $\momentum$. Note for a given mass and vector momentum, the energy could be positive or negative, the latter is unphysical. We shall define energy to be positive, $$\pm p^4 = E = +\sqrt{m^2 + \| \momentum \|^2}. \eqno(3.4b)$$

Substitution $\phi=\cos{(p_{\mu}x^{\mu})}$ into eq. (3.2b) yields a multivector solution to the Dirac eq. (3.2a) which can be expressed in the exponential form[@Pezz8301][@Ross], $$\eigen{\Psi}(x) =
\exp{(-\phat \ p_{\mu}x^{\mu})}\  \Lambda, \eqno(3.5a)$$ $$\phat=m^{-1} {\bf p} =
