Hamiltonian formalism for charged-particle systems interacting with absorptive dielectrics

We use the auxiliary field method to obtain a quantized Hamilton formalism for charged particles interacting with absorptive dielectrics. We give various equivalent representations. For absorptive dielectrics extending over all space, such as absorptive photonic crystals, our formalism is equivalent to that of Dung et al. [Phys. Rev. A 65, 043813 (2002)]. We also show that, as for nonabsorptive photonic crystals, to leading order the excited states of embedded two-level atoms do not decay radiatively if their transition frequencies are in a band gap