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v3.3.2
The effective action approach for finding the conductivity tensor is considered. The general theory is applied to the calculation of the Casimir energy and force of the Dirac material, namely graphene. The scattering theory to find an expression for the Casimir energy in terms of the Fresnel reflection matrices is used. Three problems are discussed in detail. The Casimir-Polder energy and Casimir torque for anisotropic molecules close to planar material in particular graphene. The theory is applied to the case of CO$_2$ gas and possible filtration of air with graphene as a filter. The second problem, the Casimir energy and force for a stack of conductive planes (in particular graphene), is considered in detail. The last is the dynamical Casimir effect for laterally moving graphene.