Abstract

We consider the vacuum energy for a scalar field subject to a frequency dependent boundary condition. The effect of a frequency cutoff is described in terms of an incomplete ? function. The use of the Debye asymptotic expansion for Bessel functions allows us to determine the dominant (volume, area, . . .) terms in the Casimir energy. The possible interest of this kind of model for dielectric media (and its application to sonoluminescence) is also discussed. ©2000 The American Physical Society.