Alternative effective Hamiltonians in nonrelativistic quantum electrodynamics

We consider, in the context of nonrelativistic quantum electrodynamics, the transformation from the minimal-coupling Hamiltonian to one where the interaction is quadratic in the electromagnetic vector potential. The new effective Hamiltonian is used to obtain the energy shifts in an atom caused by its interaction with the electromagnetic field. This demonstration is very compact since all the terms contributing to the shift arise from the single quadratic-coupling Hamiltonian. A brief comparison with other Hamiltonians having alternative couplings is made.