The Dirac Equation in a Curved Space of Constant Curvature

The Dirac equation is derived in a curved space of constant curvature. The underlying space is discussed on the basis of projective geometry. The pseudo-distance is introduced in the space and a particular coordinate system is adopted which may be identified with the angular part of the polar coordinate system in a five-dimensional Euclidean space. For the derivation of the Dirac equation in our curved . space two alternative methods are applied: In one method the parallelism of vector is used to derive the covariant derivatives of the spinors and in another the covariant derivative is derived from the integrability conditions of the generalized Dirac matrix.