Effective Lagrangians of the electromagnetic field in dispersive media

Electromagnetic field in dispersive dielectric media can be described in the framework of effective field theory. The interaction between the electromagnetic field and the medium on microscopic level is described by a modified Hopfield Lagrangian. The effective theory is obtained by elimination of the matter degrees of freedom, by means of the functional integration over the matter fields. From the effective Lagrangian, that describes the properties of the medium, we can obtain eg. an expression for the frequency dependent dielectric constant. The nonlinearity of the dielectric medium we treat as a perturbation since in this case the functional integration can not be performed using Gaussian integrals.