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An equivalence principle for electromagnetics through Clifford’s geometric algebras, doi:10.1016/j.metmat.2008.03.002

Ribeiro, M. ; Paiva, C. R.

Metamaterials Vol. 2, Nº --, pp. 77 - 91, September, 2008.

ISSN (print): 1873-1988
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Journal Impact Factor: 0,344 (in 2015)

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Abstract
As already pointed out by several authors, a given electromagnetic medium creates an effec-tive geometry and a given geometry creates an effective medium – what we call the equiva-lence principle for electromagnetics. This bears some resemblance to the kinematic aspects of the interaction between masses and the spacetime metric of general relativity. In this article, using Clifford’s geometric algebras defined over the tangent and cotangent bundles of space-time, we generalize the topological interpretation of this equivalence principle: introducing a transformation that we call the vacuum form reduction, we are led to a fictitious spacetime corresponding to a special class of bianisotropic media (in the materials interpretation) and which reduces to spacetime vacuum as a particular case (in the topological interpretation). We illustrate our theoretical approach with two examples: transformation and moving media.