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arXiv · 1808.01652

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

Vladimir V. Kassandrov·Joseph A. Rizcallah
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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.

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Vladimir V. Kassandrov, Joseph A. Rizcallah. 2018-08-05. Self-Dual Connections and the Equations of Fundamental Fields in a Weyl-Cartan Space. https://doi.org/10.1134/s1063779618010203

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