Casimir energy of \(N\) \(\delta\)-plates with constant conductivity

The Casimir energy for \(N\) \(\delta\)-function plates depends on multiple scattering parameter \(\Delta\). This \(N\) body interaction was distributed into two body interactions with nearest neighbour scattering and next-to-nearest neighbour scattering based on partitions of \(N-1\) and its permutations. Implementing this methodology, we investigate Casimir energy for multiple plates with constant conductivity relatable to Graphene. We also study Casimir interaction between a perfect magnetic conductor and multiple constant conductivity \(\delta\) plates, which results in Boyer repulsion. In the asymptotic limit for ideal boundary conditions, the results become simple where multiple scattering parameter \(\Delta\) consists only of nearest neighbour scattering term.