A diagrammatic expansion of the Casimir energy in multiple reflections: theory and applications

We develop a diagrammatic representation of the Casimir energy of a multibody
configuration. The diagrams represent multiple reflections between the objects
and can be organized by a few simple rules. The lowest-order diagrams (or
reflections) give the main contribution to the Casimir interaction which proves
the usefulness of this expansion. Among some applications of this, we find
analytical formulae describing the interaction between "edges", i.e.
semi-infinite plates, where we also give a first example of blocking in the
context of the Casimir energy. We also find the interaction of edges with a
needle and describe analytically a recent model of the repulsion due to the
Casimir interaction.