General Solutions of One Class of Field Equations

Abstract

We find general solutions of some field equations (systems of equations) in pseudo-Euclidian spaces (so-called primitive field equations). These equations are used in the study of the Dirac equation and Yang-Mills equations. These equations are invariant under orthogonal O(p,q) coordinate transformations and invariant under gauge transformations, which depend on some Lie groups. In this paper we use some new geometric objects - Clifford field vector and an algebra of h-forms which is a generalization of the algebra of differential forms and the Atiyah-K\"{a}hler algebra.