Fourth order perturbative expansion for the Casimir energy with a slightly deformed plate

C. FOSCO; F. LOMBARDO; F.D. MAZZITELLI

PHYSICAL REVIEW D

AMER PHYSICAL SOC

Lugar: New York; Año: 2012 vol. 86 p. 125018 - 125028

1550-7998

We apply a perturbative approach to evaluate the Casimir energy for a massless real scalar field in 3 þ 1 dimensions, subject to Dirichlet boundary conditions on two surfaces. One of the surfaces is assumed to be flat, while the other corresponds to a small deformation, described by a single function , of a flat mirror. The perturbative expansion is carried out up to the fourth order in the deformation , and the results are applied to the calculation of the Casimir energy for corrugated mirrors in front of a plane. We also reconsider the proximity force approximation within the context of this expansion.