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

CESAR D. FOSCO, FERNANDO C. LOMBARDO AND FRANCISCO D. MAZZIRELLI

PHYSICAL REVIEW D - PARTICLE AND FILDS

APS

Lugar: Nueva York; Año: 2012 vol. 86 p. 1250181 - 12501810

0556-2821

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.