Holomorphy in Pseudo-Euclidean Spaces and the Classic Electromagnetic Theory

"Professor George C. Moisil, In Memoriam"

  • Vlad L. Negulescu no affiliation
Keywords: holomorphy in pseudo-Euclidean spaces, holomorphic functions, general pseudo-rotation matrix, extended Cauchy-Riemannn differential equations, extended Poisson’s equations, electro-magnetic scalar and vector potentials, the charge conservation and general Maxwell equations

Abstract

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.

References

(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

Published
2019-11-08