Derivative expansion for the electromagnetic and Neumann-Casimir effects in 2+1 dimensions with imperfect mirrors

C. D. FOSCO, F. C. LOMBARDO, AND F. D. MAZZITELLI

PHYSICAL REVIEW D - PARTICLE AND FILDS

American Institute of Physics

Lugar: New York; Año: 2015 vol. 91 p. 1050191 - 1050199

0556-2821

We calculate the Casimir interaction energy in d 1⁄4 2 spatial dimensions between two (zero-width) mirrors?one flat and the other slightly curved?upon which 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 nonanalyticity 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 true also for the scalar field model.