Rumsey’s reaction concept generalized

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. The medium is assumed homogeneous and isotropic in this paper.