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arXiv · 2311.14027

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

Vladimir V. Kassandrov·Joseph A. Rizcallah·Ivan A. Matveev
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Abstract

We briefly present our version of noncommutative analysis over matrix algebras, the algebra of biquaternions ($\mathbb B$) in particular. We demonstrate that any $\mathbb B$-differentiable function gives rise to a null shear-free congruence (NSFC) on the $\mathbb B$-vector space $\mathbb{C}\bf M$ and on its Minkowski subspace $\bf M$. Making use of the Kerr--Penrose correspondence between NSFC and twistor functions, we obtain the general solution to the equations of $\mathbb B$-differentiability and demonstrate that the source of an NSFC is, generically, a world sheet of a string in $\mathbb {C}\bf M$. Any singular point, caustic of an NSFC, is located on the complex null cone of a point on the generating string. Further we describe symmetries and associated gauge and spinor fields, with two electromagnetic types among them. A number of familiar and novel examples of NSFC and their singular loci are described. Finally, we describe a conservative algebraic dynamics of a set of identical particles on the ``Unique Worldline'' and discuss the connections of the theory with the Feynman--Wheeler concept of ``One-Electron Universe''

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BibTeXRIS

Vladimir V. Kassandrov, Joseph A. Rizcallah, Ivan A. Matveev. 2023-11-23. Algebrodynamics: Shear-Free Null Congruences and New Types of Electromagnetic Fields. https://doi.org/10.3390/axioms12111061

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