Rumsey's Reaction Concept Generalized
Classical Physics
2020-12-03 v2
Abstract
The reaction concept, introduced by Rumsey in 1954, describes interaction between time-harmonic electromagnetic sources through the fields radiated by the sources. In the original form the concept was a scalar quantity defined by three-dimensional field and source vectors. In the present paper, the representation is extended to four dimensions applying differential-form formalism. It turns out that, in a coordinate-free form, the reaction concept must actually be a one-form, whose temporal component yields Rumsey's scalar reaction. The spatial one-form component corresponds to a three-dimensional Gibbsian-vector reaction which consists of electromagnetic force terms.
Cite
@article{arxiv.1909.08506,
title = {Rumsey's Reaction Concept Generalized},
author = {Ismo V. Lindell and Ari Sihvola},
journal= {arXiv preprint arXiv:1909.08506},
year = {2020}
}
Comments
6 pages. sign errors corrected in Eqs. (54), (55) and (56)