Self-Dual Connections and the Equations of Fundamental Fields in a Weyl-Cartan Space

Abstract

Spaces with a Weyl-type connection and torsion of a special type induced by the structure of the differentiability conditions in the algebra of complex quaternions are considered. The consistency of these conditions implies the self-duality of curvature. The Maxwell and SL(2, C) Yang-Mills fields associated with the irreducible components of the connection also turn out to be self-dual, so that the corresponding equations are fulfilled on the solutions of the generating system. Using the twistor structure of the latter, its general solution is obtained. The singular locus has a string-like (particle-like) structure and generates the self-consistent algebraic dynamics of the string system.

4 pages. Report at the International Session-Conference "Physics of Fundamental Interactions". Dubna, Apr. 12-15, 2016

References in corpus (5)

• Algbrodynamics over complex space and phase extension of the Minkowski geometry
• Collective Lorentz invariant dynamics on a single "polynomial" worldline
• Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence
• Double gauge invariance and covariantly-constant vector fields in Weyl geometry
• Relativistic Algebra of Space-Time and Algebrodynamics

Cited by in corpus (1)

• Algebrodynamics: Shear-Free Null Congruences and New Types of Electromagnetic Fields