Casimir Interaction of Chern–Simons Layers on Substrates via Vacuum Stress Tensor

Abstract

We develop a Green’s functions scattering method for systems with Chern–Simons plane boundary layers on dielectric half-spaces. The Casimir pressure is derived by evaluation of the stress tensor in a vacuum slit between two half-spaces. The sign of the Casimir pressure on a Chern–Simons plane layer separated by a vacuum slit from the Chern–Simons layer at the boundary of a dielectric half-space is analyzed for intrinsic Si and SiO2 glass substrates.