Holomorphy in Pseudo-Euclidean Spaces and the Classic Electromagnetic Theory
"Professor George C. Moisil, In Memoriam"
A new concept of holomorphy in pseudo-Euclidean spaces is briefly presented. The set of extended Cauchy-Riemannn differential equations, which are verified by the holomorphic functions, is obtained. A form of the general pseudo-rotation matrix was developed. The generalized d’Alembert- operator and extended Poisson’s equations are defined. Applying these results to the relativistic space-time, the charge conservation and general Maxwell equations are derived.
(1) N. Salingaros, Electromagnetism and the holomorphic properties of spacetime, J.Math.Phys. 22, 1919-1925 (1981).
(2) K.Guerlebeck and W. Sproessig, Quaternionic and Clifford calculus for physicists and engineers (Cichester, Wiley, 1997).
(3) Geometrized Units System, http://en.wikipedia.org/wiki/Geometrized_unit_system (accessed May 25, 2019)
(4) R. Adler, M. Bazin, M. Schiffer, Introduction to general relativity (New York, McGraw-Hill, 1965)
(5) Vlad L. Negulescu, Motion analysis of particles using the hyper-complex numbers representation, Open Access Journal of Mathematical and Theoretical Physics, Volume 2, Issue 1, 2019, https://medcraveonline.com/OAJMTP/OAJMTP-02-00047.pdf
(6) R.P. Feynman, R.B. Leighton, M. Sands, The Feynman lectures on physics, 2. Mainly electromagnetism and matter (Reading, Mass., Addison-Wesley, 1969).
(7) Oleg D. Jefimenko, On the Relativistic Invariance of Maxwell’s Equations, Z. Naturforsch. 54a, 637-644 (1999, http://zfn.mpdl.mpg.de/data/Reihe_A/54/ZNA-1999-54a-0637.pdf
Copyright (c) 2019 Vlad L. Negulescu
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors wishing to include figures, tables, or text passages that have already been published elsewhere are required to obtain permission from the copyright owner(s) for both the print and online format and to include evidence that such permission has been granted when submitting their papers. Any material received without such evidence will be assumed to originate from the authors.
All authors of manuscripts accepted for publication in the journal Transactions on Networks and Communications are required to license the Scholar Publishing to publish the manuscript. Each author should sign one of the following forms, as appropriate:
License to publish; to be used by most authors. This grants the publisher a license of copyright. Download forms (MS Word formats) - (doc)
Publication agreement — Crown copyright; to be used by authors who are public servants in a Commonwealth country, such as Canada, U.K., Australia. Download forms (Adobe or MS Word formats) - (doc)
License to publish — U.S. official; to be used by authors who are officials of the U.S. government. Download forms (Adobe or MS Word formats) – (doc)
The preferred method to submit a completed, signed copyright form is to upload it within the task assigned to you in the Manuscript submission system, after the submission of your manuscript. Alternatively, you can submit it by email firstname.lastname@example.org