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

E. N. Bukina·V. M. Dubovik
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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~\cite{French} about 40 years ago are given in this paper for the first time.

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E. N. Bukina, V. M. Dubovik. 1998-11-13. The gauge freedoms of enlarged Helmholtz theorem and the Neumann --- Debye potentials; their manifestation in the multipole expansion of conserved current. https://arxiv.org/abs/math-ph/9811011

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