Casimir energy of concentric and infinite cylindrical shells of perfect conductor

Abstract

We investigate the Casimir energy, due to the zero-point vacuum fluctuations, in a space which is cut into parts by the concentric and infinite cylindrical shells which are perfectly conductive. The Casimir energy turns out to be convergent. A interesting decomposition for the Casimir energy is found during the renormalization with the Zeta function regularization. For the double-layer shells it is decomposed into three independent and convergent parts that are from the interior, exterior cylindrical shells and between them, respectively. One of three parts, from between the two shells, has the property that the coefficient of the Casimir energy varies with the shell interval, comparing to the constant coefficient for a topologically similar geometry, the parallel plates. For n-layer shells, the Casimir energy consists of (2 n−1) parts all of which are convergent.