Casimir energy of N magnetodielectric δ-function plates

To investigate Casimir electromagnetic interaction in $N$ bodies, we implement multiple $\delta$-function plates with electric and magnetic properties. We use their optical properties to study the energy between by implementing scattering formalism. initially solve Green's functions for two three configurations obtain reflection coefficients. Further, coefficients are implemented formalism, a simple method was obtained depict density distribution expansions using diagrammatic loops. The bodies depends on parameter $\Delta$; this distributed into nearest neighbour next-to-nearest terms represented different loops depending reflection, transmission propagation distance. In manner, generalized identifying systematic pattern representation of