Casimir forces in a T-operator approach

We explore the scattering approach to Casimir forces. Our main tool is the description of Casimir energy in terms of transition operators. The approach is valid for scalar fields as well as for electromagnetic fields. We provide several equivalent derivations of the formula presented by Kenneth and Klich [Phys. Rev. Lett. 97, 160401 (2006)]. We study the convergence properties of the formula and how to utilize it together with scattering data to compute the force. Next, we discuss the form of the formula in special cases such as the simplified form obtained when a single object is placed next to a mirror. We illustrate the approach by describing the force between scatterers in one dimension and three dimensions, where we obtain the interaction energy between two spherical bodies at all distances. We also consider the cases of scalar Casimir effect between spherical bodies with different radii as well as different dielectric functions.