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Differential form valued forms and distributional electromagnetic sources

Research output: Contribution to journalJournal article

Published

Article number033506
Journal publication date10/03/2009
JournalJournal of Mathematical Physics
Journal number3
Volume50
Number of pages28
Original languageEnglish

Abstract

Properties of a fundamental double-form of bidegree (p,p) for p ≥ 0 are reviewed in order to establish a distributional framework for analyzing equations of the form Δ+λ2 = , where Δ is the Hodge–de Rham operator on p-forms on R3. Particular attention is devoted to singular distributional solutions that arise when the source is a singular p-form distribution. A constructive approach to Dirac distributions on (moving) submanifolds embedded in R3 is developed in terms of (Leray) forms generated by the geometry of the embedding. This framework offers a useful tool in electromagnetic modeling where the possibly time-dependent sources of certain physical attributes, such as electric charge, electric current, and polarization or magnetization, are concentrated on localized regions in space.