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A direct approach to the derivation of electric dyadic Green's functions

A straightforward yet rigorous approach that does not require distribution theory is used to derive a generalized electric dyadic Green's function which remains valid within the source region. Although the electric field expressed by the dyadic Green's function proves to be unique, the exact form of the dyadic itself depends upon the shape of its "principle volume." The dependence on principle volume is determined explicitly, and the different Green's dyadics derived by previous authors are shown to emerge merely through the appropriate choice for the principle volumes.