Casimir Energy of an irregular membrane

Abstract

We compute the Casimir energy which arises in a bi-dimensional surface due to the quantum fluctuations of a scalar field. We assume that the boundaries are irregular and the field obeys Dirichlet condition. We re-parametrize the problem to one which has flat boundary conditions and the irregularity is treated as a perturbation in the Laplace-Beltrami operator which appears. Later, to compute the Casimir energy, we use zeta function regularization. It is compared the results coming from perturbation theory with the WKB method.