Differential Forms in Electromagnetics

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Functional analysis and exterior calculus on mixed-dimensional geometries (2017, methodology): “We refer the reader to more comprehensive texts for a complete introduction (some instructive and relevant works are [1, 3, 10, 18, 22, 32], noting that in general throughout the text we will mostly be consistent with the notation as used in [3] with the exception that for a manifold i , we denote t”
Perfect Electromagnetic Conductor (2005, methodology): “Denoting by | the scalar product between multivectors and dual multivectors of the same grade [2, 3], the most general linear relation between the two electromagnetic two-forms has the form Ψ = M|Φ, (5) where M is the medium dyadic involving 36 scalar parameters [3].”
Transformation method for problems involving perfect electromagnetic conductor (PEMC) structures (2005, background): “It has been previously pointed out that, assuming (8), there arises a contradiction between the two Maxwell equations when assuming general sources in the medium [7], [8].”
Realization of the PEMC boundary (2005, background): “These conditions have a basic theoretical interest because, in differential-form formalism [2], [3], they correspond to the simplest possible medium defined by a single scalar medium parameter [1].”