Towards a factorization of M4

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Abstract
It may be desirable to eliminate M4 as the underlying manifold in which some physical theories are cast, and recast these theories in the space ’’√M4.’’ We investigate some of the properties of one such space, which we denote by S8. S8 can be coordinatized by real eight-component spinors. The spinor algebra on this space is developed in this paper. It is shown that a (nondegenerate) spinor in S8 determines an orthogonal tetrad on M4 (the set of these spinors determines the space of orthogonal frames over M4), and that this spinor corresponds to a ’’particle.’’ A simple geometrical interpretation of the Dirac equation arises in arriving at this correspondence.

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