Abstract
The matrices of elementary particles are generalized to general coordinates, and a new covariant displacement operator is defined, in order to generalize the theory of elementary particles to general relativity, and obtain general commutation rules. The elementary particle is considered as a singularity, with spinstructure of a gravitational field which gives Riemannian structure to the space-time. It is shown that the transformation properties of the space-time are determined not only by the affine structure due to the gravitational field but also by the spin-structure of the particle singularity.

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