Casimir-Lifshitz pressure on cavity walls

We extend our previous work on the electromagnetic Casimir-Lifshitz interaction between two bodies when one is contained within other. focus fluctuation-induced pressure acting cavity wall, which assumed to be spherical. This can positive or negative depending response functions describing and medium filling cavity. However, we find that, under general hypotheses, sign independent of geometry configuration. result based representation energy in terms transition operators. In particular, study components these operators related inside scattering amplitudes, adapting invariant imbedding procedure this unfamiliar setup. that main agreement with Dzyaloshinskii-Lifshitz-Pitaevskii result, obtained as a limiting case.