The general path-integral formulation was set up for Casimir energy of the electromagnetic gauge field. By separating into transversal electric and magnetic modes, the problem was reduced to two decoupled problems for scalar fields which differ only in their boundary conditions. In each case, the Casimir energy was calculated for general plate deformations perturbatively. Results on both the normal and the lateral force between sinusoidally corrugated plates were outlined.
Thorsten Emig, et. al., (2003) Normal and lateral Casimir forces between deformed plates.Physical Review A - Atomic, Molecular, and Optical Physics67:2022114/15. DOI: http://doi.org/10.1103/PhysRevA.67.022114
Physical Review A - Atomic, Molecular, and Optical Physics