Dispersion Interactions in a Molecular Crystal

We implement a microsopic theory of polarization and magnetization, formulated within non-relativistic quantum electrodynamics, to study radiative corrections to the electronic energy levels of a molecular crystal, arising from interactions between the charge-current distribution and quantum vacuum fluctuations of the electromagnetic field. To leading order in the fine structure constant, our renormalized level shift is valid for both electronic ground and excited states, and for an arbitrary number of lattice sites, including N-body interactions for all positive integers N. In particular, our expression is a sum of one-body (on-site) terms, which are a direct generalization of Bethe's result for the Lamb shift in atomic Hydrogen, and additional terms corresponding to many-body intermolecular dispersion interactions between the lattice sites. Being formulated in terms of microscopic polarization and magnetization fields, we can expand our level shift in a sum of contributions coming from an arbitrary number of electric and magnetic multipole moments, so that individual multipole transitions can be isolated and studied.