Multivector Solutions to the Hyper-Holomorphic Massive Dirac Equation

Attention is given to the interface of mathematics and physics, specifically noting that fundamental principles limit the usefulness of otherwise perfectly good mathematical general integral solutions. A new set of multivector solutions to the meta-monogenic (massive) Dirac equation is constructed which form a Hilbert space. A new integral solution is proposed which involves application of a kernel to the right side of the function, instead of to the left as usual. This allows for the introduction of a multivector generalization of the Feynman Path Integral formulation, which shows that particular ``geometric groupings'' of solutions evolve in the manner to which we ascribe the term ``quantum particle''. Further, it is shown that the role of usual $i$ is subplanted by the unit time basis vector, applied on the right side of the functions. Summary of talk, to appear in: Proceedings of the 17th Annual Lecture Series in the Mathematical Sciences, April 8-10, 1993, University of Arkansas, `Clifford Algebas in Analysis', J. Ryan, editor (CRC Press, expected 1994)