Macroscopic quantization in quantum optics and cavity quantum electrodynamics: Interatomic interactions

We extend previous work on macroscopic canonical quantization leading to a multipolar Hamiltonian appropriate for application to quantum optics and cavity QED situations involving classical optical devices. In particular, we show that the electric displacement is the negative of the conjugate momentum field and that the Coulomb and polarization energies are equal to the sum of intra-atomic Coulomb and polarization energies and interatomic contact energies. The quantum Hamiltonian is now in a form in which the theory is manifestly gauge invariant