Effective Hamiltonians in Nonrelativistic Quantum Electrodynamics

In this paper, we consider some second-order effective Hamiltonians describing the interaction of quantum electromagnetic field with atoms or molecules in nonrelativistic limit. Our procedure is valid only for off-energy-shell processes, specifically virtual processes such as those relevant ground-state energy shifts and dispersion van der Waals Casimir-Polder interactions, while on-energy-shell are excluded. These allow a considerable simplification calculation radiative shifts, dispersion, including presence boundary conditions. They can also provide clear physical insights into involved. We clarify that form Hamiltonian depends on states considered, consequently different expressions be obtained, each them well-defined range validity possible applications. apply our results to specific cases, mainly Lamb shift, atom-surface interaction, interactions between atoms, molecules, or, general, polarizable bodies.