Electromagnetic field in the Majorana--Oppenheimer formalism in the anti de Sitter Universe

E. M. Ovsiyuk

Problemy fiziki, matematiki i tehniki, no. 3 (2015), pp. 21-25.

Résumé

Exact solutions with spherical symmetry of the Maxwell equations in the oscillating anti de Sitter Universe are constructed. 3-Dimensional complex formalism by Majorana–Oppenheimer, generalized to pseudo-Riemannian space-time models in accordance with the tetrad method, is applied. The established dependence of the constructed solutions on the time variable leads to independence of the Pointing vector on time. This means that the change in time of the anti de Sitter geometry cannot be seen by measuring the energy flow density.

Détail

Keywords: Maxwell's equations, tetrad formalism, anti de Sitter Universe, non-static coordinates, complex formalism of the Majorana–Oppenheime
Mots-clés : exact solutionsr.

Bibliographie

[1] H. Weber, Die partiellen Differentialgleichungen der mathematischen Physik nach Riemann's Vorlesungen, Friedrich Vieweg und Sohn, Braunschweig, 1901

[2] L. Silberstein, “Elektromagnetische Grundgleichungen in bivectorieller Behandlung”, Ann. Phys. (Leiptzig), 22 (1907), 579–586 | DOI | Zbl

[3] L. Silberstein, “Nachtrag zur Abhandlung Uber elektromagnetische Grundgleichungen in bivektorieller Behandlung”, Ann. der Phys., 24 (1907), 783–784 | DOI | Zbl

[4] L. Silberstein, The Theory of Relativity, Macmillan, London, 1914 | Zbl

[5] H. Bateman, The Mathematical Analysis of Electrical and Optical Wave-Motion on the Basis of Maxwells Equations, University Press, Cambridge, 1915

[6] E. Majorana, Scientific Papers (unpublished). Deposited at the «Domus Galileana», Pisa, quaderno 2, p. 101/1; 3, p. 11, 160; 15, p. 16;17, p. 83, 159

[7] J. Oppenheimer, “Note on Light Quanta and the Electromagnetic Field”, Phys. Rev., 38 (1931), 725–746 | DOI

[8] I. Bialynicki-Birula, “On the Wave Function of the Photon”, Acta Phys. Polon., 86 (1994), 97–116

[9] I. Bialynicki-Birula, “Photon Wave Function”, Progress in Optics, 36 (1996), 248–294

[10] W. A. Rodrigues, E. C. de Oliveira, The Many Faces of Maxwell, Dirac and Einstein Equations, Lecture Notes in Physics, 722, Springer, 2007 | DOI | MR | Zbl

[11] A. A. Bogush, G. G. Krylov, E. M. Ovsiyuk, V. M. Red'kov, “Maxwell Equations in Complex form of Majorana–Oppenheimer, Solutions with Cylindric Symmetry in Riemann $S_3$ and Lobachevsky $H_3$ spaces”, Ricerche di matematica, 59:1 (2010), 59–96 | DOI | MR | Zbl

[12] V. M. Red'kov, N. G. Tokarevskaya, G. J. Spix, “Majorana–Oppenheimer Approach to Maxwell Electrodynamics. Part I: Minkowski Space”, Adv. Appl. Clifford Algebras, 22 (2012), 1129–1149 | DOI | MR | Zbl

[13] V. M. Red'kov, N. G. Tokarevskaya, G. J. Spix, “Majorana–Oppenheimer Approach to Maxwell Electrodynamics. Part II: Curved Riemannian Space”, Adv. Appl. Clifford Algebras, 23 (2013), 165–178 | DOI | MR | Zbl

[14] V. M. Redkov, E. M. Ovsiyuk, Quantum mechanics in spaces of constant curvature, Nova Science Publishers, Inc., New York, 2012, 434 pp.

[15] E. Ovsiyuk, V. Redkov, Elektrodinamika Maksvella v prostranstve s neevklidovoi geometriei, 2-e izd., LAP LAMBERT Academic Publishing, Deutschland, 2012, 242 pp.

[16] S. W. Hawking, G. F. R. Ellis, The large scale structure of space-time, University Press, Cambridge, 1973 | MR | Zbl

[17] O. V. Veko, N. D. Vlasii, E. M. Ovsiyuk, V. M. Red'kov, Yu. A. Sitenko, “Electromagnetic Field on de Sitter Expanding Universe: Majorana–Oppenheimer Formalism, Exact Solutions in non-Static Coordinates”, Nonlinear Phenomena in Complex Systems, 17:1 (2014), 17–39 | Zbl

[18] M. N. Olevskii, “Triortogonalnye sistemy v prostranstvakh postoyannoi krivizny, v kotorykh uravnenie $\Delta_2U+\lambda U=0$ dopuskaet polnoe razdelenie peremennykh”, Mat. sb., 27 (1950), 379–426 | MR | Zbl