Abstract. We compute the vacuum energy of a massless scalar field obeying a Robin boundary condition ((∂/∂ x) = β ) on one plate and the Dirichlet boundary condition ( = 0) on a parallel plate. The Casimir energy density for general dimension is obtained as a function of a (the plate separation) and β by studying the cylinder kernel (alias an exponential ultraviolet cutoff); we construct an infinite-series solution as a sum over classical paths and observe that the method of construction has broader applications. The total Casimir energy is finite after subtraction of divergences associated with the individual plates, which do not affect the force between the plates. The series for the total energy is an alternative to the integral formula of Romeo and Saharian, with which it agrees numerically.

Received 1 May 2006
Published 20 October 2006