The gauge freedoms of enlarged Helmholtz theorem and Debye potentials; their use in the multipole expansion of conserved current

Authors: ELENA N. BUKINA, VLADIMIR M. DUBOVIK

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 conserved electromagnetic current. 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 [1] about 40 years ago are given in this paper for the first time.

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