The gauge freedoms of enlarged Helmholtz theorem and the Neumann --- Debye potentials; their manifestation in the multipole expansion of conserved current
Abstract
We discuss gauge freedom within the scope of the enlarged Helmholtz theorem and Neumann-Debye decomposition and then demonstrate its realization for the multipole expansion of a electromagnetic current with distinguished toroid moment family. The exact solution to the latter problem was obtained in 1974, but answers to some purely mathematical questions raised by I.B.~French and Y.~Shimamoto~French about 40 years ago are given in this paper for the first time.
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