Quantum electrodynamics in a cavity

The theory of interaction of atoms and molecules with radiation confined in a cavity is presented. The effect of the confinement on the field commutation relations is examined and the modified commutation relations are derived for an arbitrary cavity. It is shown that a canonical transformation on the minimal-coupling Hamiltonian for such systems leads to a new Hamiltonian containing explicitly neither the interatomic nor the atom image potentials. The new multipolar Hamiltonian is used to calculate energy shifts of an atom and a pair of atoms near a conducting wall. Changes in the rate of spontaneous emission from an excited atom are also evaluated.