Regularization of the multipolar form of quantum electrodynamics

The multipolar form of quantum electrodynamics has been proposed by Power, Zienau et al. It is widely used in nonrelativistic calculations but has the deficiency: its Hamiltonian has a divergent operator term. In this paper, it is shown that the divergency can be removed by a regularization of the unitary transformation which converts the Coulomb gauge into the multipolar form. The regularized multipolar form is proven to have the same ultraviolet radiative divergencies as the Coulomb gauge electrodynamics. It is also demonstrated that the interaction with soft photons is represented by the usual electric dipole term eqE and interatomic Coulomb interactions persist to be absent