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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)

R2 v1 2026-06-23T11:19:19.231Z