Canonical theory of electromagnetic field quantization in dielectrics

Abstract

We introduce a fully canonical theory for QED in a lossy dispersive dielectric without recourse to the detailed properties of the material medium and its interaction with the radiation field. The formalism relies only on the causal behavior of the medium by assuming that its dielectric function necessarily satisfies the Kramers–Kronig relations. This scheme is based on the Lagrangian approach and it is shown that the field operators are those given by the Green function method of the electromagnetic field quantization. Special attention is paid to the form of the Hamiltonian with which the coupling process of the dressed annihilation and creation operators as well as the dispersion relations are clarified. We also impose appropriate limits to display the consistency check of the formulation for nondissipative media and free space.