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"Spineurs simples", "Urfelder" and factorizations of Dirac equations and spinors

Ordinary spinors are not primitive geometric objects, but derive from Cartan's "spineurs simples" (or "pure spinors"), which form non linear spaces of much lower dimensions. In turn, the latters' components are pfaffians, i.e., have the structure of v.e.v.'s of "Urfelder" of some sort, which satisfy simple equations in their own spaces. This permits factorizations of Dirac equations and their solutions, many of which unconventional; examples are given. This formalism is part of phase space geometrization of quantum mechanics; it may not be incongruent with standard approaches to particle theories.