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A topological theory of the electromagnetic-field



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Fernández-Rañada, Antonio (1989) A topological theory of the electromagnetic-field. Letters in Mathematical Physics, 18 (2). pp. 97-106. ISSN 0377-9017

Official URL: http://dx.doi.org/10.1007/BF00401864



It is shown that Maxwell equations in vacuum derive from an underlying topological structure given by a scalar field ϕ which represents a map S 3×R→S 2 and determines the electromagnetic field through a certain transformation, which also linearizes the highly nonlinear field equations to the Maxwell equations. As a consequence, Maxwell equations in vacuum have topological solutions, characterized by a Hopf index equal to the linking number of any pair of magnetic lines. This allows the classification of the electromagnetic fields into homotopy classes, labeled by the value of the helicity. Although the model makes use of only c-number fields, the helicity always verifies ∫ A·Bd3 r=nα, n being an integer and α an action constant, which necessarily appears in the theory, because of reasons of dimensionality.

Item Type:Article
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© 1989 Kluwer Academic Publishers.

Subjects:Sciences > Physics > Electricity
Sciences > Physics > Electronics
ID Code:25219
Deposited On:06 May 2014 08:27
Last Modified:10 Dec 2018 14:58

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