Electromagnetic field quantization in a linear isotropic dielectric

A macroscopic electromagnetic field is quantized in a linear isotropic dielectric by the association of a damped quantum-mechanical harmonic oscillator with each mode of the radiation field. The macroscopic Langevin equation is used to describe the motion of a damped oscillator. We discuss a fully canonical approach for the quantization of a harmonic oscillator with damping subjected to a Langevin force operator. The conjugate momentum is defined in the usual way and the quantum-mechanical Hamiltonian is introduced. This provides us with a direct method for the quantization of the radiation field in a dielectric material. Special attention is paid to the decomposition of the radiation field into transverse and longitudinal parts and their difference is elucidated by this approach.