Chiral Maxwell’s Equations as Two Spinor System: Dirac and Majorana Neutrino

DOI: 10.4236/jemaa.2013.56042   PDF   HTML   XML   6,007 Downloads   8,005 Views   Citations


This work clarifies the relation between Maxwell, Dirac and Majorana neutrino equations presenting an original way to derive the Dirac and neutrino equation from the chiral electrodynamics leading, perhaps, to novel conception in the mass generation by electromagnetic fields. In the present article, it is shown that Maxwell equations can be written in the same form as the two components Dirac and neutrino equations, that is the vector representation of electromagnetic theory can be factorized into a pair of two-component spinor field equations. We propose a simple approach with the electric field E parallel to the magnetic field H. Our analysis is based on the chiral or Weyl form of the Maxwell equations in a chiral vacuum. This theory is a new quantum mechanics (QM) interpretation for Dirac and neutrino equation. The below research proves that the QM of particles represents the electrodynamics of the curvilinear closed chiral waves. Electromagnetic properties of neutrinos are discussed.

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H. Torres-Silva, "Chiral Maxwell’s Equations as Two Spinor System: Dirac and Majorana Neutrino," Journal of Electromagnetic Analysis and Applications, Vol. 5 No. 6, 2013, pp. 264-270. doi: 10.4236/jemaa.2013.56042.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] G. R. da Rocha, I. L. Freire R. da Rocha, et al., “Spacetime Deformations and Electromagnetism in Material Media,” Hadronic Journal, Vol. 30, No. 2, 2007, pp. 417-446.
[2] Y. Tamayama, et al., “Observation of Brewster’s Effect for Transverse Electric Electromagnetic Waves in Meta materials: Experiment and Theory,” Physical Review B, Vol. 73, No. 19, 2006, Article ID: 193104. doi:10.1103/PhysRevB.73.193104
[3] Y. Tamayama, et al., “An Invisible Medium for Circularly Polarized Electromagnetic Waves,” Optics Express, Vol. 16, No. 25, 2008, pp. 20869-20875. doi:10.1364/OE.16.020869
[4] Y. Tamayama, et al., “No-Reflection Phenomena for Chi ral Media,” In: A. Petrin Ed., Wave Propagation, InTech, Rijeka, 2011, pp. 415-432. doi:10.5772/13828
[5] J. K. Gansel, et al., “Gold Helix Photonic Metamaterial as Broadband Circular Polarizer,”Science, Vol. 325, No. 6047, 2009, pp. 1513-1515. doi:10.1126/science.1177031
[6] M. Thiel, et al., “Three-Dimensional Chiral Photonic Superlattices,” Optics Letters, Vol. 35, No. 2, 2010, pp. 166-168. doi:10.1364/OL.35.000166
[7] A. Gsponer, “On the Equivalence of the Maxwell and Dirac Equations,” International Journal of Theoretical Physics, Vol. 41, No. 4, 2002, pp. 689-694. doi:10.1023/A:1015232427515
[8] W. I. Fushchyld, “On the Connection between Solutions of Dirac and Maxwell Equations,” In: W. I. Fushchyld, Ed., Scientific Works, Vol. 4, 2002, pp. 320-336.
[9] V. V. Dvoeglazov, “Generalized Maxwell and Weyl Equations for Massless Particles,” Revista Mexicana de Física, Vol. 49S1, 2003, pp. 99-103.
[10] R. H. Good, “Particle Aspect of the Electromagnetic Field Equations,” Physical Review, Vol. 105, No. 6, 1957, pp. 1914-1919. doi:10.1103/PhysRev.105.1914
[11] H. E. Moses, “Solution of Maxwell’s Equations in Spinor Notation,” Physical Review, Vol. 113, No. 6, 1959, pp 1670-1679. doi:10.1103/PhysRev.113.1670
[12] T. Vachaspati, “Maxwell Equations in the Form of Two Component Equations,” Proceedings of the Indian National Science India, Vol. 26 A, No. 4, 1959, pp. 359-363.
[13] A. Lakhtakia, “Beltrami Fields in Chiral Media,” World Scientific Series in Contemporary Chemical Physics, Vol. 2, No. 1, 1994, pp. 7-34.
[14] H. Torres-Silva and D. Torres, “Chiral Current in a Graphene Battery,” Journal of Electromagnetic Analysis and applications, Vol. 4, No. 10, 2012, pp. 426-431.
[15] H. Torres-Silva, “Chiral Dirac Equation Derived from Quaternionic Maxwell’s Systems,” Journal of Electromagnetic Analysis and applications, Vol. 5, No. 3, 2013. doi:10.4236/jemaa.2013.53017
[16] H. Torres-Silva, “Chiral Transverse Electromagnetic Standing Waves with E II H in the Dirac Equation and the Spectra of the Hydrogen Atom,” In: A. Akdagli, Ed., Behavior of Electromagnetic Waves in Different Media and Structures, Chapter 15, Book Intech, 2011, pp. 301-324.
[17] H. Torres-Silva and D. Torres Cabezas, “Chiral Seismic Attenuation with Acoustic Metamaterials,” Journal of Electromagnetics Analysis and Applications, Vol. 5, No. 1, 2013, pp. 10-15. doi:10.4236/jemaa.2013.51003
[18] L. Landau, “On the Conservation Laws for Weak Interaction,” Nuclear Physics, Vol. 3, No. 1, 1957, pp. 127-131. doi:10.1016/0029-5582(57)90061-5
[19] T. D. Lee and C. N. Yang, “Parity Non-Conservation and a Two-Component Theory of the Neutrino,” Physical Re view, Vol. 105, No. 5, 1957, pp. 1671-1675. doi:10.1103/PhysRev.105.1671
[20] A. Salam, “on Parity Conservation and Neutrino Mass,” Nuovo Cimento, Vol. 5, No. 1, 1957, pp. 299-301. doi:10.1007/BF02812841
[21] P. M. A. Dirac, “The Quantum Theory of the Electron,” Proceedings of the Royal Society of London Series A, Containing Papers of a Mathematical and Physical Character, Vol. 117, No. 778, 1928, pp. 610-616. doi:10.1098/rspa.1928.0023
[22] E. Majorana, “Teoria Simmetrica Dell’ Elettrone E Del Positrone,” Il Nuovo Cimento (1924-1942), Vol. 14, No. 4, 1937, pp. 171-184. doi:10.1007/BF02961314
[23] W. Pauli, “Zur Quantenmechanik des Magnetischen Elektrons,” Zeitschrift für Physik A Hadrons and Nuclei, Vol. 43, No. 9-10, 1927, pp. 601-623. doi:10.1007/BF01397326
[24] C. Giunti and C. W. Kim, “Fundamentals of Neutrino Physics and Astrophysics,” Oxford University Press, Ox ford.
[25] S. Bilenky, “Introduction to the Physics of Massive and Mixed Neutrinos,” Lecture Notes in Physics, Vol. 817, 2010. doi:10.1007/978-3-642-14043-3
[26] N. F. Bell, et al., “How Magnetic is the Dirac Neutrino?” Physical Review Letters, Vol. 95, 2005, Article ID: 151 802.
[27] H. Torres-Silva, “Physical Interpretation of the Dirac Equation with Electromagnetic Mass,” The Scitech, Journal of Science & Technology, 2012, pp. 127-133.
[28] A. Studenikin, “Neutrino Magnetic Moment,” Nuclear Physics B, Vol. 188, No. 1, 2009, pp. 220-222.
[29] J. Casanova, et al., “Quantum Simulation of the Majorana Equation and Unphysical Operations,” Physical Review X, Vol. 1, No. 2, 2011, Article ID: 021018. doi:10.1103/PhysRevX.1.021018
[30] L. Rozena, et al, “Violation of Heisenbergs’s Measurement-Disturbance Relationship by Weak Measurements,” Physical Review Letters, Vol. 109, 2012, Article ID: 100-404.
[31] J. Erhart, et al., “Experimental Demonstration of a Universally Valid Error-Disturbance Uncertainty Relation in Spin Measurements”, Nature Physics, Vol. 8, 2012, pp 185-189. doi:10.1038/nphys2194

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