As well-known the dynamical interaction theory of molecules or atoms with the electromagnetic field may be based alternatively on one of two HAMILTONians, IH or IIH. where the vector potential appears in the interaction term of IH while this of IIH is expressed in terms of the electric and the magnetic field strength coupled to atomic multipoles.

Using a calculus of transversal functional derivation with respect to a vector function we show that we can go from IH to IIH by a comperatively simple canonical transformation which may be interpreted within the classical theory as well as within as the quantized theory.

The equivalence of both HAMILTONians is lost if, as customary in quantum optics, only a few atomic levels are taken into account. We give a plausible argument that in this case the multipole HAMILTONian IIH is more suitable.