Casimir energy of $N$ magnetodielectric $δ$-function plates

Venkat Abhignan

Published 2023-04-20Version 1

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 Casimir energy between the plates by implementing multiple scattering formalism. We initially solve Green's functions for two and three plates configurations to obtain their reflection coefficients. Further, the coefficients are implemented in multiple scattering formalism, and a simple method was obtained to depict energy density distribution in the multiple scattering expansions using diagrammatic loops. The idea of deriving Casimir energy was extended to $N$ plates by identifying a systematic pattern.