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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.26 n.1 Antofagasta mayo 2007 

Proyecciones Journal of Mathematics
Vol. 26, No 1, pp. 105-142, May 2007.
Universidad Católica del Norte
Antofagasta - Chile





Pontificia Universidad Católica de Valparaiso, Chile.

Correspondencia a:


This work explores what other mathematical possibilities were available to Maxwell for formulating his electromagnetic field model, by characterizing the family of mathematical models induced by the analytical equations describing electromagnetic phenomena prevailing at that time.

The need for this research stems from the article "Inertial Relativity - A Functional Analysis Review", recently published in "Proyecciones", which claims and demonstrates the existence of an axiomatic conflict between the special and general theories of relativity on one side, and functional analysis on the other, making the reformulation of the relativistic theories, mandatory. As will be shown herein, such reformulation calls for a revision of Maxwell's electromagnetic field model.

The conclusion is reached that -given the set of equations considered by Maxwell- not a unique, but an infinite number of mathematically correct reformulations to Ampere's law exists, resulting in an equally abundant number of potential models for the electromagnetic phenomena (including Maxwell's). Further experimentation is required in order to determine which is the physically correct model.



[1] Sainz, Norberto. "Inertial Relativity - A Functional Analysis Review". Proyecciones (Antofagasta), ago. 2005, Vol. 24, No.2, pp. 121-152. ISSN 0716-0917.         [ Links ]

[2] Einstein, Albert. "Zur Elektrodynamik Bewegter Kórper", §3. Spanish translation by Fidel Alsina F. and Damián Canales F. of original paper published in Annalen der Physik 17, 891 (1905). "La Relatividad", Emecé Editores, B. Aires, (1950).         [ Links ]

[3] Ibid. [6], §6.

[4] Einstein, Albert. "Die Grundlage Der AUgemeinen Relativitátstheorie", §2-4. Spanish translation by Fidel Alsina F. and Damián Canales F. of original paper published in Annalen der Physik 49, 769 (1916). "La Relatividad", Emecé Editores, B. Aires, (1950).         [ Links ]

[5] Maxwell, James. "A Dynamical Theory of the Electromagnetic Field". Edition by T. Torrance of original paper published in Philosophical Transactions of the Royal Society of London 155, 459-512 (1865). Wipf & Stock Publications, Eugene, OR, (1996).         [ Links ]

[6] Hertz, Heinrich. "Untersuchungen über die Ausbreitung der Elek-trischen Kraft", English translation by D.E. Jones of Hertz' 1982 collection of publications in Wiedemann's Annalen. "Electric Waves", Macmillan and Co., London, (1893).         [ Links ]

[7] Ibid. [5] (3.34) pp 49.

[8] Maxwell, James. "A Treatise on Electricity and Magnetism". Oxford, at the Clarendon Press, (1873).         [ Links ]

[9] Ampére, A.-M. "Sur la théorie mathématique des phénoménes électrodyna-miques uniquement déduite de 1'experience", Mém. Acad. R. Sci. Inst. France, ser.2, 6, pp. 175-388, (1827).         [ Links ]

[10] Neumann, F.E. "Allgemeine Gesetze der inducirten elektriche Stróme", Abh. K. Akad. Wiss. Berlin, pp. 1-87, (1845).         [ Links ]

[11] Neumann, F.E. "Uber ein allgemeines Princip der mathematischen Théorie inducirter electricher Stróme", Abh. K. Akad. Wiss. Berlin, pp. 1-72, (1847).         [ Links ]

[12] Weber, W. "I. Elektrodynamische Maassbestimmungen", Ann. Phys. Chem. 73, pp. 193-240, 1848. (Shortened version of the 1846 paper published in Abh. K. Sáchsischen Geseflschaft Wiss., Leipzig 1846).         [ Links ]

[13] Weber, W. Elektrodynamische Maassbestimmungen (Weidmann, Leipzig). (A collection of seven papers, with the same main title but different subtitles, dating from 1846 to 1878. The first part, pp. 1-170, is from Abh. K. Sáchsischen Geseflschaft Wiss., Leipzig, 1846).

[14] Helmholtz, H. "Ueber die Bewegungsgleichungen der Elektricitat für ruhende leitende Kórper". J. Reine Angew. Math. 72, pp. 57-129, (1870).         [ Links ]

[15] Faddeev, L. D., Popov, V. N. "Feynman diagrams for the Yang-Mills fields", Phys. Lett. B 25, pp. 29-30, (1967).         [ Links ]

[16] Schoenmaker, W., Magnus, W., Meuris, P., "Ghost fields in classical gauge theories", Phys. Rev. Lett. 88 (18), (2002).         [ Links ]

[17] Lorentz, H. A. "La théorie électromagnétique de Maxwell et son application aux corps movants". Arch. Néerl. Se. 25, pp. 363-552, (1892).         [ Links ]

[18] Ibid. [8]; pp 231.

[19] Ibid. [8]; pp 232.

[20] Ibid. [8]; pp 229.

[21] Boudenot, J.-C. "Ampere au coeur de la physique du debut du XlXéme siécle". Repére: L'histoire de l'électricité. REE Revue de l'Electricité et de l'Électronique No 05, mai, (2003).         [ Links ]

[22] Thidé, Bo. "Electromagnetic Field Theory", pp 6-10. Upsilon Books, Uppsala University, Sweden, (1997).         [ Links ]

[23] Fock, V. "Uber die invariante Form der Wellen- und der Bewegungsgleichungen für einen geladenen Massenpunkt", Z. Phys. 39, pp. 226-232, (1926).         [ Links ]

[24] Jackson, J. D., Okun, L. B. "Historical roots of gauge invariance", Reviews of Modern Physics 73, pp. 663-680, (2001).         [ Links ]


Pontificia Universidad Católica de Valparaiso
Facultad de Ingeniería
Escuela de Ingeniería Industrial
Escuela de Ingeniería Eléctrica
Avda. Brasil 2241
Valparaiso - Chile
e-mail : norberto.sainz@ucv.el

Received : December 2006. Accepted : March 2007

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