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Gauge transformation leaves the electric and the magnetic fields unchanged aslong as the gauge function is treated classically. In this paper we considerthe gauge transformation commonly used to obtain the electric dipoleinteraction Hamiltonian in a system of dipoles and the electromagnetic field(Goeppert-Mayer transformation) and treat the vector potential that appear inthe gauge function as an operator. While it modifies the electric field, thestatic interaction between the dipoles is derived.

Deriving the static interaction between electric dipoles via the quantum gauge transformation