  Nonlocal Hamiltonians are used widely in first-principles quantum
calculations; the nonlocality stems from eliminating undesired degrees of
freedom, e.g. core electrons. To date, attempts to couple nonlocal systems to
external electromagnetic (EM) fields have been heuristic or limited to weak or
long wavelength fields. Using Feynman path integrals, we derive an exact,
closed-form coupling of arbitrary EM fields to nonlocal systems. Our results
justify and clarify the couplings used to date and are essential for systematic
computation of linear and especially nonlinear response.
