{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:45:43Z","timestamp":1760132743738,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,20]],"date-time":"2023-11-20T00:00:00Z","timestamp":1700438400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We briefly present our version of noncommutative analysis over matrix algebras, the algebra of biquaternions (B) in particular. We demonstrate that any B-differentiable function gives rise to a null shear-free congruence (NSFC) on the B-vector space CM and on its Minkowski subspace M. Making use of the Kerr\u2013Penrose correspondence between NSFC and twistor functions, we obtain the general solution to the equations of B-differentiability and demonstrate that the source of an NSFC is, generically, a world sheet of a string in CM. 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 \u201cUnique Worldline\u201d and discuss the connections of the theory with the Feynman\u2013Wheeler concept of \u201cOne-Electron Universe\u201d.<\/jats:p>","DOI":"10.3390\/axioms12111061","type":"journal-article","created":{"date-parts":[[2023,11,20]],"date-time":"2023-11-20T10:32:32Z","timestamp":1700476352000},"page":"1061","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Algebrodynamics: Shear-Free Null Congruences and New Types of Electromagnetic Fields"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8277-9139","authenticated-orcid":false,"given":"Vladimir V.","family":"Kassandrov","sequence":"first","affiliation":[{"name":"Institute of Gravitation and Cosmology, Peoples\u2019 Friendship University of Russia, Miklukho-Maklaya Str., 6, Moscow 117198, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8661-9004","authenticated-orcid":false,"given":"Joseph A.","family":"Rizcallah","sequence":"additional","affiliation":[{"name":"School of Education, Lebanese University, Beirut P.O. Box 6573\/14, Lebanon"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2005-9467","authenticated-orcid":false,"given":"Ivan A.","family":"Matveev","sequence":"additional","affiliation":[{"name":"Federal Research Center \u201cComputer Science and Control\u201d of the Russian Academy of Sciences, Vavilov Str., 44\/2, Moscow 119333, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Penrose, R., and Rindler, W. (1986). Spinor and Twistor Methods in Space\u2013Time Geometry, Cambridge University Press.","DOI":"10.1063\/1.2815249"},{"key":"ref_2","unstructured":"Burinskii, A.Y., and Kerr, R.P. (1995). Nonstationary Kerr congruences. arXiv."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/BF00759485","article-title":"Singularities in the Kerr-Schild metrics","volume":"10","author":"Kerr","year":"1979","journal-title":"Gen. Relativ. 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