ABSTRACT
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 is 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.
