Dual Vector Spaces and Physical Singularities Available to Purchase

Though 3‐D vector space has no mechanism within itself for creating fundamental particle singularities, this can be accomplished by a commutative combination of two 3‐D vector spaces, each of which is dual (in a physical sense) to the other. The resulting combination leads to a nilpotent quantum mechanics / quantum field theory, which incorporates exact supersymmetry and removes the anomalies due to self‐interaction. Such spin $12$ for fermions, zitterbewegung and Berry phase become natural consequences of the dual space formalism.