Clifford's structure and Clifford's differentiation on Riemannian spaces (Q1358353)

In the article is shown that on any Riemannian or pseudo-Riemannian space there naturally arises a Clifford algebra. The exterior differentiation operator in this algebra is generalized with regard to the Riemannian metric. The suggested operator of Clifford's differentiation is used to write the basic field theory equations, namely the Maxwell, Proca, Weyl, and Dirac equations in a unified coordinate-free form. With the aid of the operator of Clifford's covariant differentiation, the Clifford curvature operator is constructed.