Scattering Approach to Casimir Force
Casimir force between multiple objects of different shapes and material properties can be related to classical scattering amplitudes of electromagnetic fields from individual bodies.
"Scattering theory approach to electrodynamic Casimir forces,"
S.J. Rahi, T. Emig, N. Graham, R.L. Jaffe, and M. Kardar, Phys. Rev. D 80, 085021 (2009)
Shapes amenable to exact treatment of electromagnetic scattering:
Plane, sphere, cylinder (circular, parabolic, elliptic), wedge, cone, ...
Interior/Exterior: Can deal with objects inside one another
Babinet Principle: Relating scattering and force from screens and apertures.
Finite size/Edge effects: Role of boundaries and their interactions.
Earnshaw's Theorem: Constraints on stable equilibrium.
Off Equilibrium: Heat transfer and radiation.