Derivative expansion for the electromagnetic and Neumann Casimir effects in dimensions with imperfect mirrors
arXiv:1503.02913 · doi:10.1103/PhysRevD.91.105019
Abstract
We calculate the Casimir interaction energy in spatial dimensions between two (zero-width) mirrors, one flat, and the other slightly curved, upon which {\em imperfect\/} conductor boundary conditions are imposed for an Electromagnetic (EM) field. Our main result is a second-order Derivative Expansion (DE) approximation for the Casimir energy, which is studied in different interesting limits. In particular, we focus on the emergence of a non-analyticity beyond the leading-order term in the DE, when approaching the limit of perfectly-conducting mirrors. We also show that the system considered is equivalent to a dual one, consisting of a massless real scalar field satisfying imperfect Neumann conditions (on the very same boundaries). Therefore, the results obtained for the EM field hold also true for the scalar field model
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