d^3\vector{P} \over {(2\pi)^3}}
\ \exp{[-\basis{4}\ p^{\mu}(x_{\mu}-x^{\prime}_{\mu})}]. \eqno(4.9b)$$ It can be easily shown[@Pezz8301] that this propagator may be written in the [PIF]{} form of eq. (4.8a) with the replacement: $i\rightarrow -\basis{4}$. Further, the other half of the solution space, the negative parity solutions (‘antiparticles’) will follow the same relation, except requiring the replacement $\basis{4}\rightarrow\ -\basis{4}$ in eq. (4.9b) and $i \rightarrow +\basis{4}$ in eq. (4.8a).

Summary
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We are not aware of any other work in Clifford analysis that has considered the [PIF]{} (Path Integral Formulation) of kernels. This approach suggests that the particular form of eq. (3.7a) is the “special” multigeometric entity which propagates (unchanged) in the manner to which we ascribe the term “quantum particle”. Further, the [PIF]{} provides a method to introduce interactions into the quantum equation based upon classical mechanics. Because of eq. (4.9a), we see that the interactions will couple [*dextrally*]{} to the wavefunction (multiplied on the right). In particular, the generator of electromagnetic interactions will be $\basis{4}$ applied on the right[@Pezz9302]. Finally, separate from these physical interpretations, the general mathematical relationship between the “right-side applied” [*dextrad kernel*]{} introduced in eq. (4.9a) and the standard “left-side applied” one of eq. (4.3a) \[both as an integral solutions 