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 non-flat 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 associated to the coordinate transformation. Later, to compute the Casimir energy, we use zeta function regularization. It is compared with the results coming from perturbation theory with the one from Wentzel-Kramers-Brillouin (WKB) method.