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-Kähler algebra.

22 pages

Cited by in corpus (8)

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• Stochastic Levy Differential Operators and Yang-Mills Equations
• On constant solutions of $\mathrm{SU}(2)$ Yang-Mills equations with arbitrary current in Euclidean space ${\mathbb{R}}^n$
• Levy Laplacians in Hida calculus and Malliavin calculus
• Classification of extended Clifford algebras
• On analysis in differential algebras and modules
• Development of the Method of Averaging in Clifford Geometric Algebras
• Classification of all constant solutions of $\mathrm{SU}(2)$ Yang-Mills equations with arbitrary current in pseudo-Euclidean space ${\mathbb{R}}^{p,q}$